Mots-clés : lens space
@article{VCHGU_2015_17_a8,
author = {M. Mulazzani and E. Manfredi},
title = {On knots and links in lens spaces},
journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
pages = {118--134},
year = {2015},
number = {17},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a8/}
}
TY - JOUR AU - M. Mulazzani AU - E. Manfredi TI - On knots and links in lens spaces JO - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika PY - 2015 SP - 118 EP - 134 IS - 17 UR - http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a8/ LA - en ID - VCHGU_2015_17_a8 ER -
M. Mulazzani; E. Manfredi. On knots and links in lens spaces. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 118-134. http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a8/
[1] K. Baker, J. E. Grigsby, M. Hedden, “Grid diagrams for lens spaces and combinatorial knot Floer homology”, Int. Math. Res. Not. (IMRN), 10 (208), art. ID rnm024 | MR
[2] J. Berge, Some knots with surgeries yielding lens spaces, Unpublished
[3] S. Stevan, Torus Knots in Lens Spaces Topological Strings, arXiv: 1308.5509
[4] D. Buck, M. Mauricio, “Connect sum of lens spaces surgeries: application to Hin recombination”, Math. Proc. Cambridge Philos. Soc., 150 (2011), 505–525 | DOI | MR | Zbl
[5] S. Lambropoulou, C. P. Rourke, “Markov's theorem in 3-manifolds”, Topology Appl., 78 (1997), 95–122 | DOI | MR | Zbl
[6] J. Hoste, J. H. Przytycki, “The $(2,\infty)$-skein module of lens spaces; a generalization of the Jones polynomial”, J. Knot Theory Ramifications, 2 (1993), 321–333 | DOI | MR | Zbl
[7] B. Gabrovšek, Classification of knots in lens spaces, Ph D. Thesis, University of Ljubljana, Slovenia, 2013
[8] E. Manfredi, Knots and links in lens spaces, Ph D. Thesis, University of Bologna, Italy, 2014
[9] E. Manfredi, “Lift in the $3$-sphere of knots and links in lens spaces”, J. Knot Theory Ramifications, 23 (2014), 1450022 | DOI | MR | Zbl
[10] S. V. Matveev, “Distributive groupoids in knot theory”, Math. USSR Sb., 47 (1984), 73–83 | DOI | Zbl
[11] A. Cattabriga, E. Manfredi, M. Mulazzani, “On knots and links in lens spaces”, Topology Appl., 160 (2013), 430–442 | DOI | MR | Zbl
[12] C. Cornwell, “A polynomial invariant for links in lens spaces”, J. Knot Theory Ramifications, 21 (2012), 1250060 | DOI | MR | Zbl
[13] A. Cattabriga, E. Manfredi, L. Rigolli, Equivalence of two diagram representations of links in lens spaces and essential invariants, arXiv: 1312.2230 | MR
[14] E. J. Brody, “The topological classification of the lens spaces”, Ann. of Math., 71 (1960), 163–184 | DOI | MR | Zbl
[15] F. Bonahon, “Diffótopies des espaces lenticulaires”, Topology, 22 (1983), 305–314 | DOI | MR | Zbl
[16] C. Hodgson, J. H. Rubinstein, Involutions and isotopies of lens spaces, Springer Publ., Berlin, 1985 | MR
[17] Y. V. Drobotukhina, “An analogue of the Jones polynomial for links in $\mathbb{R}P^{3}$ and a generalization of the Kauffman–Murasugi theorem”, Leningrad Math. J., 2 (1991), 613–630 | MR | Zbl
[18] M. Sakuma, “Uniqueness of symmetries of knots”, Math. Z., 192 (1986), 225–242 | DOI | MR | Zbl
[19] M. Boileau, E. Flapan, “Uniqueness of free actions on $\mathbf{S}^3$ respecting a knot”, Canad. J. Math., 39 (1987), 969–982 | DOI | MR | Zbl
[20] R. Fenn, C. Rourke, “Racks and links in codimension two”, J. Knot Theory Ramifications, 1 (1992), 343–406 | DOI | MR | Zbl
[21] D. V. Gorkovets, “Cocycle invariants for links in projective space”, Vestn. Chelyab. Gos. Univ. Mat. Mekh. Inform., 12 (2010), 88–97 | MR
[22] D. V. Gorkovets, “Distributive groupoids for knots in projective space”, Vestn. Chelyab. Gos. Univ. Mat. Mekh. Inform., 10 (208), 89–93 | MR | Zbl
[23] J. Scott Carter, “A survey of quandle ideas”, Introductory lectures on knot theory., Knots Everything, 46, World Sci. Publ., Hackensack, NJ, 2012 | MR | Zbl
[24] V. Q. Huynh, T. T. Q. Le, “Twisted Alexander polinomial of links in the projective space”, J. Knot Theory Ramifications, 17 (2008), 411–438 | DOI | MR | Zbl
[25] F. H. Norwood, “Every two-generator knot is prime”, Proc. Amer. Math. Soc., 86 (1982), 143–147 | DOI | MR | Zbl
[26] M. Wada, “Twisted Alexander polynomial for finitely presentable groups”, Topology, 33 (1994), 241–256 | DOI | MR | Zbl
[27] S. Friedl, S. Vidussi, “A survey of twisted Alexander polynomials”, Contrib. Math. Comput. Sci., 2011, Springer, Heidelberg | MR | Zbl
[28] C. H. Dowker, M. B. Thistlethwaite, “Classifications of knot projections”, Topology Appl., 16 (1983), 19–31 | DOI | MR | Zbl
[29] H. Doll, J. Hoste, “A tabulation of oriented link”, Math. Comp., 57 (1991), 747–761 | DOI | MR | Zbl
[30] N. Chbili, “A new criterion for knots with free periods”, Ann. Fac. Sci. Toulouse Math., 12 (2003), 465–477 | DOI | MR | Zbl
[31] J. A. Hillman, C. Livingston, S. Naik, “Twisted Alexander polynomials of periodic knots”, Algebr. Geom. Topol., 6 (2006), 145–169 | DOI | MR | Zbl
[32] N. Chbili, “The multi-variable Alexander polynomial of lens braids”, J. Knot Theory Ramifications, 11 (2002), 1323–1330 | DOI | MR | Zbl