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Journal articles on the topic 'Knot Floer'

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Published: 10 March 2023

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1

Ni, Yi. "Knot Floer homology detects fibred knots." Inventiones mathematicae 170, no. 3 (September 20, 2007): 577–608. http://dx.doi.org/10.1007/s00222-007-0075-9.

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2

Ni, Yi. "Knot Floer homology detects fibred knots." Inventiones mathematicae 177, no. 1 (February 13, 2009): 235–38. http://dx.doi.org/10.1007/s00222-009-0174-x.

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3

ROBERTS, LAWRENCE. "ON KNOT FLOER HOMOLOGY FOR SOME FIBERED KNOTS." Communications in Contemporary Mathematics 15, no. 01 (January 22, 2013): 1250053. http://dx.doi.org/10.1142/s0219199712500538.

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We use knot Floer surgery exact sequences and torsion invariants to compute the knot Floer homology of certain fibered knots in the double cover of S3 branched along the closure of an alternating braid.
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4

BALDWIN, JOHN A., and WILLIAM D. GILLAM. "COMPUTATIONS OF HEEGAARD-FLOER KNOT HOMOLOGY." Journal of Knot Theory and Its Ramifications 21, no. 08 (May 10, 2012): 1250075. http://dx.doi.org/10.1142/s0218216512500757.

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We compute the knot Floer homology of knots with at most 12 crossings, as well as the τ invariant for knots with at most 11 crossings, using the combinatorial approach described by Manolescu, Ozsváth and Sarkar. We review their construction, giving two examples that can be workout out by hand, and we explain some ideas we used to simplify the computation. We conclude with a discussion of knot Floer homology for small knots, and we formulate a conjecture about the behavior of knot Floer homology under mutation, paying especially close attention to the Kinoshita–Terasaka knot and its Conway mutant. Finally, we discuss a conjecture of Rasmussen on relationship between Khovanov homology and knot Floer homology, and observe that it is consistent with our calculations.
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5

SAHAMIE, BIJAN. "SYMMETRIES AND ADJUNCTION INEQUALITIES FOR KNOT FLOER HOMOLOGY." Journal of Knot Theory and Its Ramifications 21, no. 10 (July 11, 2012): 1250104. http://dx.doi.org/10.1142/s0218216512501040.

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We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots. Furthermore, we obtain an adjunction inequality for cobordism maps in knot Floer homologies. We demonstrate the adjunction inequalities and symmetries in explicit calculations which recover some of the main results from [E. Eftekhary, Longitude Floer homology and the Whitehead double, Algebr. Geom. Topol. 5 (2005) 1389–1418] on longitude Floer homology and also give rise to vanishing results on knot Floer homologies.
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6

Goda, Hiroshi, Hiroshi Matsuda, and Takayuki Morifuji. "Knot Floer Homology of (1, 1)-Knots." Geometriae Dedicata 112, no. 1 (April 2005): 197–214. http://dx.doi.org/10.1007/s10711-004-5403-2.

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7

Ng, Lenhard, Peter Ozsváth, and Dylan Thurston. "Transverse knots distinguished by knot Floer homology." Journal of Symplectic Geometry 6, no. 4 (2008): 461–90. http://dx.doi.org/10.4310/jsg.2008.v6.n4.a4.

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8

Hom, Jennifer. "A survey on Heegaard Floer homology and concordance." Journal of Knot Theory and Its Ramifications 26, no. 02 (February 2017): 1740015. http://dx.doi.org/10.1142/s0218216517400156.

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In this survey paper, we discuss several different knot concordance invariants coming from the Heegaard Floer homology package of Ozsváth and Szabó. Along the way, we prove that if two knots are concordant, then their knot Floer complexes satisfy a certain type of stable equivalence.
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9

Paolo Ghiggini. "Knot Floer homology detects genus-one fibred knots." American Journal of Mathematics 130, no. 5 (2008): 1151–69. http://dx.doi.org/10.1353/ajm.0.0016.

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10

Tobin, Joshua P. "Knot Floer filtration classes of topologically slice knots." Journal of Knot Theory and Its Ramifications 23, no. 09 (August 2014): 1450047. http://dx.doi.org/10.1142/s0218216514500473.

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The knot Floer complex and the concordance invariant ε can be used to define a filtration on the smooth concordance group. We exhibit an ordered subset of this filtration that is isomorphic to ℕ × ℕ and consists of topologically slice knots.
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11

BAO, YUANYUAN. "ON THE KNOT FLOER HOMOLOGY OF A CLASS OF SATELLITE KNOTS." Journal of Knot Theory and Its Ramifications 21, no. 04 (April 2012): 1250030. http://dx.doi.org/10.1142/s0218216511009807.

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Knot Floer homology is an invariant for knots in the three-sphere for which the Euler characteristic is the Alexander–Conway polynomial of the knot. The aim of this paper is to study this homology for a class of satellite knots, so as to see how a certain relation between the Alexander–Conway polynomials of the satellite, companion and pattern is generalized on the level of the knot Floer homology. We also use our observations to study a classical geometric invariant, the Seifert genus, of our satellite knots.
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12

Cha, Jae Choon, and Toshifumi Tanaka. "Classical homological invariants are not determined by knot Floer homology and Khovanov homology." Journal of Knot Theory and Its Ramifications 25, no. 07 (June 2016): 1650039. http://dx.doi.org/10.1142/s0218216516500395.

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We illustrate that there are knots for which Heegaard knot Floer homology and Khovanov homology are identical but the Alexander module and torsion invariants differ. The examples are certain symmetric unions. We also give examples of similar flavor, concerning the Kauffman and Q-polynomials in place of the classical homological invariants. This shows there are nonmutant knots with the same knot Floer and Khovanov homology.
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13

Krcatovich, David. "The reduced knot Floer complex." Topology and its Applications 194 (October 2015): 171–201. http://dx.doi.org/10.1016/j.topol.2015.08.008.

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14

LI, WEIPING. "EQUIVARIANT KNOT SIGNATURES AND FLOER HOMOLOGIES." Journal of Knot Theory and Its Ramifications 10, no. 05 (August 2001): 687–701. http://dx.doi.org/10.1142/s0218216501001098.

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In this paper, we give a description of the equivariant signature of knots from the symplectic topology point of view. For certain knots K in S3, we define a symplectic Floer homology for the representation space of the knot group π1 (S3\ K) into SU(2) with trace [Formula: see text] along all meridians (p is an odd prime and 0<k<p). The symplectic Floer homology of knots is a new invariant of knots and its Euler number is half of the equivariant signature of knots.
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15

Park, Kyungbae. "On independence of iterated Whitehead doubles in the knot concordance group." Journal of Knot Theory and Its Ramifications 27, no. 01 (January 2018): 1850003. http://dx.doi.org/10.1142/s0218216518500037.

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Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.
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16

Vafaee, Faramarz. "On the Knot Floer Homology of Twisted Torus Knots." International Mathematics Research Notices 2015, no. 15 (August 21, 2014): 6516–37. http://dx.doi.org/10.1093/imrn/rnu130.

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17

Eftekhary, Eaman. "Floer homology and splicing knot complements." Algebraic & Geometric Topology 15, no. 6 (December 31, 2015): 3155–213. http://dx.doi.org/10.2140/agt.2015.15.3155.

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18

Hedden, Matthew. "Knot Floer homology of Whitehead doubles." Geometry & Topology 11, no. 4 (December 17, 2007): 2277–338. http://dx.doi.org/10.2140/gt.2007.11.2277.

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19

Lambert-Cole, Peter. "Twisting, mutation and knot Floer homology." Quantum Topology 9, no. 4 (October 31, 2018): 749–74. http://dx.doi.org/10.4171/qt/119.

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20

Zemke. "Knot Floer homology obstructs ribbon concordance." Annals of Mathematics 190, no. 3 (2019): 931. http://dx.doi.org/10.4007/annals.2019.190.3.5.

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21

Hedden, Matthew. "On knot Floer homology and cabling." Algebraic & Geometric Topology 5, no. 3 (September 20, 2005): 1197–222. http://dx.doi.org/10.2140/agt.2005.5.1197.

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22

Ozsváth, Peter, and Zoltán Szabó. "Knot Floer homology and integer surgeries." Algebraic & Geometric Topology 8, no. 1 (February 8, 2008): 101–53. http://dx.doi.org/10.2140/agt.2008.8.101.

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23

Juhasz, Andras. "Knot Floer homology and Seifert surfaces." Algebraic & Geometric Topology 8, no. 1 (May 12, 2008): 603–8. http://dx.doi.org/10.2140/agt.2008.8.603.

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24

Ozsváth, Peter S., and Zoltán Szabó. "Knot Floer homology and rational surgeries." Algebraic & Geometric Topology 11, no. 1 (January 6, 2010): 1–68. http://dx.doi.org/10.2140/agt.2011.11.1.

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25

Ozsváth, Peter S., András I. Stipsicz, and Zoltán Szabó. "Concordance homomorphisms from knot Floer homology." Advances in Mathematics 315 (July 2017): 366–426. http://dx.doi.org/10.1016/j.aim.2017.05.017.

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26

Juhász, András, and Marco Marengon. "Concordance maps in knot Floer homology." Geometry & Topology 20, no. 6 (December 21, 2016): 3623–73. http://dx.doi.org/10.2140/gt.2016.20.3623.

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27

Kauffman, Louis H., and Marithania Silvero. "Alexander–Conway polynomial state model and link homology." Journal of Knot Theory and Its Ramifications 25, no. 03 (March 2016): 1640005. http://dx.doi.org/10.1142/s0218216516400058.

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This paper shows how the Formal Knot Theory state model for the Alexander–Conway polynomial is related to Knot Floer Homology. In particular, we prove a parity result about the states in this model that clarifies certain relationships of the model with Knot Floer Homology.
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28

Li, Weiping. "Casson-Lin's Invariant and Floer Homology." Journal of Knot Theory and Its Ramifications 06, no. 06 (December 1997): 851–77. http://dx.doi.org/10.1142/s0218216597000480.

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Casson defined an invariant which can be thought of as the number of conjugacy classes of irreducible representations of π1(Y) into SU(2) counted with signs, where Y is an oriented integral homology 3-sphere. Lin defined a similar invariant (the signature of a knot) for a braid representative of a knot in S3. In this paper, we give a natural generalization of Casson-Lin's invariant. Our invariant is the symplectic Floer homology for the representation space of π1(S3 \ K) into SU(2) with trace-zero along all meridians. The symplectic Floer homology of braids is a new invariant of knots and its Euler number is the negative of Casson-Lin's invariant.
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29

Baldwin, John, and David Vela-Vick. "A note on the knot Floer homology of fibered knots." Algebraic & Geometric Topology 18, no. 6 (October 18, 2018): 3669–90. http://dx.doi.org/10.2140/agt.2018.18.3669.

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30

Ozsváth, Peter, András I. Stipsicz, and Zoltán Szabó. "Knot lattice homology in L-spaces." Journal of Knot Theory and Its Ramifications 25, no. 01 (January 2016): 1650003. http://dx.doi.org/10.1142/s0218216516500036.

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We show that the knot lattice homology of a knot in an [Formula: see text]-space is chain homotopy equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring [Formula: see text]). Suppose that [Formula: see text] is a negative definite plumbing tree which contains a vertex [Formula: see text] such that [Formula: see text] is a union of rational graphs. Using the identification of knot homologies we show that for such graphs the lattice homology [Formula: see text] is isomorphic to the Heegaard Floer homology [Formula: see text] of the corresponding rational homology sphere [Formula: see text].
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31

WIDMER, TAMARA. "QUASI-ALTERNATING MONTESINOS LINKS." Journal of Knot Theory and Its Ramifications 18, no. 10 (October 2009): 1459–69. http://dx.doi.org/10.1142/s0218216509007518.

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The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot Floer homology detects the genus of a knot as well as whether a knot is fibered, characterization of quasi-alternating links becomes an interesting open problem. We show that there exist classes of non-alternating Montesinos links, which are quasi-alternating.
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32

Doig, Margaret I. "Finite knot surgeries and Heegaard Floer homology." Algebraic & Geometric Topology 15, no. 2 (April 22, 2015): 667–90. http://dx.doi.org/10.2140/agt.2015.15.667.

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33

Dai, Irving, Jennifer Hom, Matthew Stoffregen, and Linh Truong. "More concordance homomorphisms from knot Floer homology." Geometry & Topology 25, no. 1 (March 2, 2021): 275–338. http://dx.doi.org/10.2140/gt.2021.25.275.

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34

Manolescu, Ciprian, Peter Ozsváth, and Sucharit Sarkar. "A combinatorial description of knot Floer homology." Annals of Mathematics 169, no. 2 (March 1, 2009): 633–60. http://dx.doi.org/10.4007/annals.2009.169.633.

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35

Grigsby, J. Elisenda. "Knot Floer homology in cyclic branched covers." Algebraic & Geometric Topology 6, no. 3 (September 25, 2006): 1355–98. http://dx.doi.org/10.2140/agt.2006.6.1355.

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36

Lowrance, Adam. "On knot Floer width and Turaev genus." Algebraic & Geometric Topology 8, no. 2 (July 25, 2008): 1141–62. http://dx.doi.org/10.2140/agt.2008.8.1141.

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37

Zemke, Ian. "Connected sums and involutive knot Floer homology." Proceedings of the London Mathematical Society 119, no. 1 (January 29, 2019): 214–65. http://dx.doi.org/10.1112/plms.12227.

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38

Ozsváth, Peter, and Zoltán Szabó. "Knot Floer homology, genus bounds, and mutation." Topology and its Applications 141, no. 1-3 (June 2004): 59–85. http://dx.doi.org/10.1016/j.topol.2003.09.009.

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39

Alishahi, Akram, and Eaman Eftekhary. "Knot Floer homology and the unknotting number." Geometry & Topology 24, no. 5 (December 29, 2020): 2435–69. http://dx.doi.org/10.2140/gt.2020.24.2435.

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40

Elisenda Grigsby, J., and Stephan M. Wehrli. "On the colored Jones polynomial, sutured Floer homology, and knot Floer homology." Advances in Mathematics 223, no. 6 (April 2010): 2114–65. http://dx.doi.org/10.1016/j.aim.2009.11.002.

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41

Vance, Katherine. "Tau invariants for balanced spatial graphs." Journal of Knot Theory and Its Ramifications 29, no. 09 (August 2020): 2050066. http://dx.doi.org/10.1142/s0218216520500662.

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In 2003, Ozsváth and Szabó defined the concordance invariant [Formula: see text] for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of [Formula: see text] for knots in [Formula: see text] and a combinatorial proof that [Formula: see text] gives a lower bound for the slice genus of a knot. Recently, Harvey and O’Donnol defined a relatively bigraded combinatorial Heegaard Floer homology theory for transverse spatial graphs in [Formula: see text], extending HFK for knots. We define a [Formula: see text]-filtered chain complex for balanced spatial graphs whose associated graded chain complex has homology determined by Harvey and O’Donnol’s graph Floer homology. We use this to show that there is a well-defined [Formula: see text] invariant for balanced spatial graphs generalizing the [Formula: see text] knot concordance invariant. In particular, this defines a [Formula: see text] invariant for links in [Formula: see text]. Using techniques similar to those of Sarkar, we show that our [Formula: see text] invariant is an obstruction to a link being slice.
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42

Eftekhary, Eaman. "Knots which admit a surgery with simple knot Floer homology groups." Algebraic & Geometric Topology 11, no. 3 (May 4, 2011): 1243–56. http://dx.doi.org/10.2140/agt.2011.11.1243.

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43

Li, Weiping. "The symplectic floer homology of the square knot and granny knots." Acta Mathematica Sinica, English Series 15, no. 1 (January 1999): 1–10. http://dx.doi.org/10.1007/s10114-999-0056-6.

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44

Baldwin, John A., Adam Simon Levine, and Sucharit Sarkar. "Khovanov homology and knot Floer homology for pointed links." Journal of Knot Theory and Its Ramifications 26, no. 02 (February 2017): 1740004. http://dx.doi.org/10.1142/s0218216517400041.

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A well-known conjecture states that for any [Formula: see text]-component link [Formula: see text] in [Formula: see text], the rank of the knot Floer homology of [Formula: see text] (over any field) is less than or equal to [Formula: see text] times the rank of the reduced Khovanov homology of [Formula: see text]. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose [Formula: see text] page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field [Formula: see text].
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45

BALDRIDGE, SCOTT, and ADAM M. LOWRANCE. "CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS." Journal of Knot Theory and Its Ramifications 21, no. 05 (April 2012): 1250033. http://dx.doi.org/10.1142/s0218216511009832.

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In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under five cube diagram moves. A knot homology is constructed from cube diagrams and shown to be equivalent to knot Floer homology.
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46

DOUROUDIAN, FATEMEH. "COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS." Journal of Knot Theory and Its Ramifications 22, no. 06 (May 2013): 1350014. http://dx.doi.org/10.1142/s0218216513500144.

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47

Kim, Se-Goo, and Mi Jeong Yeon. "Rasmussen and Ozsváth–Szabó invariants of a family of general pretzel knots." Journal of Knot Theory and Its Ramifications 24, no. 03 (March 2015): 1550017. http://dx.doi.org/10.1142/s0218216515500170.

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We compute integer valued knot concordance invariants of a family of general pretzel knots if the invariants are equal to the negative values of signatures for alternating knots. Examples of such invariants are Rasmussen s-invariants and twice Ozsváth–Szabó knot Floer homology τ-invariants. We use the crossing change inequalities of Livingston and the fact that pretzel knots are almost alternating. As a consequence, for the family of pretzel knots given in this paper, s-invariants are twice τ-invariants.
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48

Truong, Linh. "Truncated Heegaard Floer homology and knot concordance invariants." Algebraic & Geometric Topology 19, no. 4 (August 16, 2019): 1881–901. http://dx.doi.org/10.2140/agt.2019.19.1881.

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49

Ozsváth, Peter, and Zoltán Szabó. "Knot Floer homology and the four-ball genus." Geometry & Topology 7, no. 2 (October 22, 2003): 615–39. http://dx.doi.org/10.2140/gt.2003.7.615.

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50

Ni, Yi. "A note on knot Floer homology of links." Geometry & Topology 10, no. 2 (June 21, 2006): 695–713. http://dx.doi.org/10.2140/gt.2006.10.695.

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