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Journal articles on the topic 'Three-manifolds'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Mednykh, A. D. "Three-dimensional hyperelliptic manifolds." Annals of Global Analysis and Geometry 8, no. 1 (January 1990): 13–19. http://dx.doi.org/10.1007/bf00055015.

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2

Matveev, S. V. "Three-manifolds. Classical results." Journal of Mathematical Sciences 74, no. 1 (March 1995): 834–60. http://dx.doi.org/10.1007/bf02362845.

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3

SONG, YI, and STEPHEN P. BANKS. "DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, HEEGAARD SPLITTINGS AND THREE-DIMENSIONAL SYSTEMS." International Journal of Bifurcation and Chaos 17, no. 06 (June 2007): 2085–95. http://dx.doi.org/10.1142/s0218127407018233.

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The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.

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4

Gordeeva, I. A., and S. E. Stepanov. "Three classes of Weitzenböck manifolds." Russian Mathematics 56, no. 1 (December 30, 2011): 83–85. http://dx.doi.org/10.3103/s1066369x12010136.

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5

Gómez-Larrañaga, José Carlos, Francisco González-Acuña, and Wolfgang Heil. "Amenable category of three–manifolds." Algebraic & Geometric Topology 13, no. 2 (March 30, 2013): 905–25. http://dx.doi.org/10.2140/agt.2013.13.905.

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6

CHO, JONG TAEK, and DONG-HEE YANG. "CONFORMALLY FLAT CONTACT THREE-MANIFOLDS." Journal of the Australian Mathematical Society 103, no. 2 (November 3, 2016): 177–89. http://dx.doi.org/10.1017/s1446788716000471.

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In this paper, we consider contact metric three-manifolds $(M;\unicode[STIX]{x1D702},g,\unicode[STIX]{x1D711},\unicode[STIX]{x1D709})$ which satisfy the condition $\unicode[STIX]{x1D6FB}_{\unicode[STIX]{x1D709}}h=\unicode[STIX]{x1D707}h\unicode[STIX]{x1D711}+\unicode[STIX]{x1D708}h$ for some smooth functions $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$, where $2h=\unicode[STIX]{x00A3}_{\unicode[STIX]{x1D709}}\unicode[STIX]{x1D711}$. We prove that if $M$ is conformally flat and if $\unicode[STIX]{x1D707}$ is constant, then $M$ is either a flat manifold or a Sasakian manifold of constant curvature $+1$. We cannot extend this result for a smooth function $\unicode[STIX]{x1D707}$. Indeed, we give such an example of a conformally flat contact three-manifold which is not of constant curvature.

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7

Singerman, D. "CLASSICAL TESSELLATIONS AND THREE-MANIFOLDS." Bulletin of the London Mathematical Society 21, no. 3 (May 1989): 292–93. http://dx.doi.org/10.1112/blms/21.3.292.

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8

Fischer, Werner. "Classical Tessellations and Three-Manifolds." Zeitschrift für Kristallographie 189, no. 1-2 (January 1989): 155. http://dx.doi.org/10.1524/zkri.1989.189.1-2.155.

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9

Matveev, S. V. "Tabulation of three-dimensional manifolds." Russian Mathematical Surveys 60, no. 4 (August 31, 2005): 673–98. http://dx.doi.org/10.1070/rm2005v060n04abeh003673.

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10

Matveev, Sergei V. "Computer Recognition of Three-Manifolds." Experimental Mathematics 7, no. 2 (January 1998): 153–61. http://dx.doi.org/10.1080/10586458.1998.10504365.

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11

Perrone, Domenico. "Homogeneous contact Riemannian three-manifolds." Illinois Journal of Mathematics 42, no. 2 (June 1998): 243–56. http://dx.doi.org/10.1215/ijm/1256045043.

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12

Calvaruso, G. "Homogeneous paracontact metric three-manifolds." Illinois Journal of Mathematics 55, no. 2 (2011): 697–718. http://dx.doi.org/10.1215/ijm/1359762409.

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13

Hamilton, M. J. D., and D. Kotschick. "Stable indecomposability of three-manifolds." Homology, Homotopy and Applications 21, no. 2 (2019): 27–28. http://dx.doi.org/10.4310/hha.2019.v21.n2.a3.

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14

Barbot, Thierry. "Three-dimensional Anosov flag manifolds." Geometry & Topology 14, no. 1 (January 2, 2010): 153–91. http://dx.doi.org/10.2140/gt.2010.14.153.

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15

Braam, Peter J. "Magnetic monopoles on three-manifolds." Journal of Differential Geometry 30, no. 2 (1989): 425–64. http://dx.doi.org/10.4310/jdg/1214443597.

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16

Hu, Zhiguang, and Shaoqiang Deng. "Three dimensional homogeneous Finsler manifolds." Mathematische Nachrichten 285, no. 10 (February 9, 2012): 1243–54. http://dx.doi.org/10.1002/mana.201100100.

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17

Kotschick, D. "Three-manifolds and Kähler groups." Annales de l’institut Fourier 62, no. 3 (2012): 1081–90. http://dx.doi.org/10.5802/aif.2717.

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18

Jacobowitz, Howard. "Locally CR spherical three manifolds." Proceedings of the American Mathematical Society 148, no. 9 (March 17, 2020): 3925–26. http://dx.doi.org/10.1090/proc/15023.

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19

Calvaruso, Giovanni. "Three-dimensional Ivanov–Petrova manifolds." Journal of Mathematical Physics 50, no. 6 (June 2009): 063509. http://dx.doi.org/10.1063/1.3152607.

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20

CALVARUSO, G., and B. DE LEO. "PSEUDO-SYMMETRIC LORENTZIAN THREE-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (November 2009): 1135–50. http://dx.doi.org/10.1142/s0219887809004132.

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We investigate pseudo-symmetric Lorentzian three-manifolds for the different possible Segre types of the Ricci operator. After determining all three-dimensional pseudo-symmetric Lorentzian algebraic curvature tensors, we classify pseudo-symmetric Lorentzian three-spaces which are either homogeneous, curvature homogeneous up to order 1 or curvature homogeneous, and we also provide some examples which are not curvature homogeneous.

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21

Willett, Brian. "Localization on three-dimensional manifolds." Journal of Physics A: Mathematical and Theoretical 50, no. 44 (October 13, 2017): 443006. http://dx.doi.org/10.1088/1751-8121/aa612f.

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22

Calviño-Louzao, E., E. García-Río, J. Seoane-Bascoy, and R. Vázquez-Lorenzo. "Three-dimensional conformally symmetric manifolds." Annali di Matematica Pura ed Applicata (1923 -) 193, no. 6 (May 24, 2013): 1661–70. http://dx.doi.org/10.1007/s10231-013-0349-3.

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23

Berndt, Jürgen. "Three-dimensional Einstein-like manifolds." Differential Geometry and its Applications 2, no. 4 (December 1992): 385–97. http://dx.doi.org/10.1016/0926-2245(92)90004-7.

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24

Martelli, Bruno, and Carlo Petronio. "Complexity of Geometric Three-manifolds." Geometriae Dedicata 108, no. 1 (October 2004): 15–69. http://dx.doi.org/10.1007/s10711-004-3181-x.

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25

Gelfand, S., and D. Kazhdan. "Invariants of three-dimensional manifolds." Geometric and Functional Analysis 6, no. 2 (March 1996): 268–300. http://dx.doi.org/10.1007/bf02247888.

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26

Neumann, Walter D., and Don Zagier. "Volumes of hyperbolic three-manifolds." Topology 24, no. 3 (1985): 307–32. http://dx.doi.org/10.1016/0040-9383(85)90004-7.

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27

Calvaruso, Giovanni. "Curvature homogeneous Lorentzian three-manifolds." Annals of Global Analysis and Geometry 36, no. 1 (November 29, 2008): 1–17. http://dx.doi.org/10.1007/s10455-008-9144-6.

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28

Cahn, Patricia, and Alexandra Kjuchukova. "Linking Numbers in Three-Manifolds." Discrete & Computational Geometry 66, no. 2 (July 6, 2021): 435–63. http://dx.doi.org/10.1007/s00454-021-00287-3.

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AbstractLet M be a connected, closed, oriented three-manifold and K, L two rationally null-homologous oriented simple closed curves in M. We give an explicit algorithm for computing the linking number between K and L in terms of a presentation of M as an irregular dihedral three-fold cover of $$S^3$$ S 3 branched along a knot $$\alpha \subset S^3$$ α ⊂ S 3 . Since every closed, oriented three-manifold admits such a presentation, our results apply to all (well-defined) linking numbers in all three-manifolds. Furthermore, ribbon obstructions for a knot $$\alpha $$ α can be derived from dihedral covers of $$\alpha $$ α . The linking numbers we compute are necessary for evaluating one such obstruction. This work is a step toward testing potential counter-examples to the Slice-Ribbon Conjecture, among other applications.

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29

Tinsley, F. C., and David G. Wright. "Some contractible open manifolds and coverings of manifolds in dimension three." Topology and its Applications 77, no. 3 (June 1997): 291–301. http://dx.doi.org/10.1016/s0166-8641(96)00122-8.

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30

Nimershiem, Barbara E. "All flat three-manifolds appear as cusps of hyperbolic four-manifolds." Topology and its Applications 90, no. 1-3 (December 1998): 109–33. http://dx.doi.org/10.1016/s0166-8641(98)00183-7.

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31

Planat, Michel, Raymond Aschheim, Marcelo Amaral, and Klee Irwin. "Universal Quantum Computing and Three-Manifolds." Symmetry 10, no. 12 (December 19, 2018): 773. http://dx.doi.org/10.3390/sym10120773.

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A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 ’s obtained from Dehn fillings are explored.

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32

Cho, Jong Taek. "NOTES ON ALMOST KENMOTSU THREE-MANIFOLDS." Honam Mathematical Journal 36, no. 3 (September 25, 2014): 637–45. http://dx.doi.org/10.5831/hmj.2014.36.3.637.

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33

Martín, Francisco, and William H. Meeks. "Calabi-Yau domains in three manifolds." American Journal of Mathematics 134, no. 5 (2012): 1329–44. http://dx.doi.org/10.1353/ajm.2012.0037.

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34

Abbaspour, Hossein. "On string topology of three manifolds." Topology 44, no. 5 (September 2005): 1059–91. http://dx.doi.org/10.1016/j.top.2005.04.003.

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35

Gabai, David, Robert Meyerhoff, and Peter Milley. "Minimum volume cusped hyperbolic three-manifolds." Journal of the American Mathematical Society 22, no. 4 (May 1, 2009): 1157–215. http://dx.doi.org/10.1090/s0894-0347-09-00639-0.

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36

Burns, Daniel M., and Charles L. Epstein. "Embeddability for three-dimensional CR-manifolds." Journal of the American Mathematical Society 3, no. 4 (1990): 809. http://dx.doi.org/10.1090/s0894-0347-1990-1071115-4.

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37

Lempert, L{ászl{ó. "On three-dimensional Cauchy-Riemann manifolds." Journal of the American Mathematical Society 5, no. 4 (1992): 923. http://dx.doi.org/10.1090/s0894-0347-1992-1157290-3.

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38

Taubes, Clifford Henry. "Book Review: Monopoles and three-manifolds." Bulletin of the American Mathematical Society 46, no. 3 (February 9, 2009): 505–9. http://dx.doi.org/10.1090/s0273-0979-09-01250-6.

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39

Shalen, Peter B. "Three-manifolds and Baumslag–Solitar groups." Topology and its Applications 110, no. 1 (January 2001): 113–18. http://dx.doi.org/10.1016/s0166-8641(99)00167-4.

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40

Mishachev, K. N. "Hamiltonian links in three-dimensional manifolds." Izvestiya: Mathematics 59, no. 6 (December 31, 1995): 1193–205. http://dx.doi.org/10.1070/im1995v059n06abeh000054.

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41

Ghosh, Nandan, and Manjusha Tarafdar. "On three dimensional quasi-Sasakian manifolds." Tbilisi Mathematical Journal 9, no. 1 (June 2016): 23–28. http://dx.doi.org/10.1515/tmj-2016-0003.

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42

Bettiol, Renato G., and Benjamin Schmidt. "Three-manifolds with many flat planes." Transactions of the American Mathematical Society 370, no. 1 (September 15, 2017): 669–93. http://dx.doi.org/10.1090/tran/6961.

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43

Gursky, Matthew, Jeffrey Streets, and Micah Warren. "Conformally bending three-manifolds with boundary." Annales de l’institut Fourier 60, no. 7 (2010): 2421–47. http://dx.doi.org/10.5802/aif.2613.

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44

Derbez, Pierre. "Local rigidity of aspherical three-manifolds." Annales de l’institut Fourier 62, no. 1 (2012): 393–416. http://dx.doi.org/10.5802/aif.2708.

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45

Schmidt, Benjamin, and Jon Wolfson. "Three-manifolds with constant vector curvature." Indiana University Mathematics Journal 63, no. 6 (2014): 1757–83. http://dx.doi.org/10.1512/iumj.2014.63.5436.

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46

Vesnin, A. Yu, V. G. Turaev, and E. A. Fominykh. "Three-dimensional manifolds with poor spines." Proceedings of the Steklov Institute of Mathematics 288, no. 1 (January 2015): 29–38. http://dx.doi.org/10.1134/s0081543815010034.

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47

Turaev, V. G. "Homeomorphisms of geometric three-dimensional manifolds." Mathematical Notes of the Academy of Sciences of the USSR 43, no. 4 (April 1988): 307–12. http://dx.doi.org/10.1007/bf01139137.

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48

Tian, Kevin T., Eric Samperton, and Zhenghan Wang. "Haah codes on general three-manifolds." Annals of Physics 412 (January 2020): 168014. http://dx.doi.org/10.1016/j.aop.2019.168014.

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49

Ivey, Thomas. "Ricci solitons on compact three-manifolds." Differential Geometry and its Applications 3, no. 4 (December 1993): 301–7. http://dx.doi.org/10.1016/0926-2245(93)90008-o.

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50

Hilden, H. M., M. T. Lozano, J. M. Montesinos, and W. C. Whitten. "On universal groups and three-manifolds." Inventiones Mathematicae 87, no. 3 (October 1987): 441–56. http://dx.doi.org/10.1007/bf01389236.

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