Relevant bibliographies by topics / Knot concordance invariants

Academic literature on the topic 'Knot concordance invariants'

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Published: 10 March 2023

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Journal articles on the topic "Knot concordance invariants"

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KEARNEY, M. KATE. "THE CONCORDANCE GENUS OF 11-CROSSING KNOTS." Journal of Knot Theory and Its Ramifications 22, no. 13 (November 2013): 1350077. http://dx.doi.org/10.1142/s0218216513500776.

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The concordance genus of a knot is the least genus of any knot in its concordance class. It is bounded above by the genus of the knot, and bounded below by the slice genus, two well-studied invariants. In this paper we consider the concordance genus of 11-crossing prime knots. This analysis resolves the concordance genus of 533 of the 552 prime 11-crossing knots. The appendix to the paper gives concordance diagrams for 59 knots found to be concordant to knots of lower genus, including null-concordances for the 30 11-crossing knots known to be slice.
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Kim, Taehee. "Knots having the same Seifert form and primary decomposition of knot concordance." Journal of Knot Theory and Its Ramifications 26, no. 14 (December 2017): 1750103. http://dx.doi.org/10.1142/s0218216517501036.

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We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not concordant to any knot with coprime Alexander polynomial. Key ingredients for the proof are Cheeger–Gromov–von Neumann [Formula: see text]-invariants for amenable groups developed by Cha–Orr and polynomial splittings of metabelian [Formula: see text]-invariants.
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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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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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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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Cochran, Tim D., and Peter Teichner. "Knot concordance and von Neumann $\rho$ -invariants." Duke Mathematical Journal 137, no. 2 (April 2007): 337–79. http://dx.doi.org/10.1215/s0012-7094-07-13723-2.

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7

Gilmer, Pat, and Charles Livingston. "An algebraic link concordance group for (p, 2p−1)-links in S2p+1." Proceedings of the Edinburgh Mathematical Society 34, no. 3 (October 1991): 455–62. http://dx.doi.org/10.1017/s0013091500005228.

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A concordance classification of links of , p < 1, is given in terms of an algebraically defined group, Φ±, which is closely related to Levine's algebraic knot concordance group. For p=1,Φ_ captures certain obstructions to two component links in S3 being concordant to boundary links, the generalized Sato-Levine invariants defined by Cochran. As a result, purely algebraic proofs of properties of these invariants are derived.
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Dasbach, Oliver T., and Adam M. Lowrance. "Turaev genus, knot signature, and the knot homology concordance invariants." Proceedings of the American Mathematical Society 139, no. 7 (December 22, 2010): 2631–45. http://dx.doi.org/10.1090/s0002-9939-2010-10698-6.

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9

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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10

Lewark, Lukas, and Andrew Lobb. "Upsilon-like concordance invariants from 𝔰𝔩n knot cohomology." Geometry & Topology 23, no. 2 (April 8, 2019): 745–80. http://dx.doi.org/10.2140/gt.2019.23.745.

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Dissertations / Theses on the topic "Knot concordance invariants"

1

Davis, Christopher. "First Order Signatures and Knot Concordance." Thesis, 2012. http://hdl.handle.net/1911/64621.

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Invariants of knots coming from twisted signatures have played a central role in the study of knot concordance. Unfortunately, except in the simplest of cases, these signature invariants have proven exceedingly difficult to compute. As a consequence, many knots which presumably can be detected by these invariants are not a well understood as they should be. We study a family of signature invariants of knots and show that they provide concordance information. Significantly, we provide a tractable means for computing these signatures. Once armed with these tools we use them first to study the knot concordance group generated by the twist knots which are of order 2 in the algebraic concordance group. With our computational tools we can show that with only finitely many exceptions, they form a linearly independent set in the concordance group. We go on to study a procedure given by Cochran-Harvey-Leidy which produces infinite rank subgroups of the knot concordance group which, in some sense are extremely subtle and difficult to detect. The construction they give has an inherent ambiguity due to the difficulty of computing some signature invariants. This ambiguity prevents their construction from yielding an actual linearly independent set. Using the tools we develop we make progress to removing this ambiguity from their procedure.
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COLLARI, CARLO. "Transverse invariants from the deformations of Khovanov sl2- and sl3-homologies." Doctoral thesis, 2017. http://hdl.handle.net/2158/1079076.

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The aim of this thesis is the study of transverse link invariants coming from Khovanov sl 2 - and sl 3 -homologies and from their deformations. As a by-product of our work we get computable estimates on some concordance invariants coming from Khovanov sl_2-homologies.
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Martin, Taylor. "Lower order solvability of links." Thesis, 2013. http://hdl.handle.net/1911/71998.

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The n-solvable filtration of the link concordance group, defined by Cochran, Orr, and Teichner in 2003, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. We focus on the first two stages of the n-solvable filtration, which are the class of 0-solvable links and the class of 0.5-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric characterization 0-solve equivalent links. As a result, we completely characterize 0-solvable links and we give a classification of links up to 0-solve equivalence. We relate 0-solvable links to known results about links bounding gropes and Whitney towers in the 4-ball. We then establish a sufficient condition for a link to be 0.5-solvable and show that 0.5-solvable links must have vanishing Sato-Levine invariants.
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"The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants." Thesis, 2011. http://hdl.handle.net/1911/70379.

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We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.
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