Algebraic & Geometric Topology Volume 23, issue 4 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Distinguishing Legendrian knots with trivial orientation-preserving symmetry group

Ivan Dynnikov and Vladimir Shastin

Algebraic & Geometric Topology 23 (2023) 1849–1889

DOI: 10.2140/agt.2023.23.1849

Bibliography

1	M Boileau, B Zimmermann, Symmetries of nonelliptic Montesinos links, Math. Ann. 277 (1987) 563 MR891592
2	F Bonahon, L C Siebenmann, New geometric splittings of classical knots and the classification and symmetries of arborescent knots, unpublished manuscript (2016)
3	Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
4	W Chongchitmate, L Ng, An atlas of Legendrian knots, Exp. Math. 22 (2013) 26 MR3038780
5	M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the topology of 3–manifolds, (2016)
6	I A Dynnikov, Arc-presentations of links: monotonic simplification, Fund. Math. 190 (2006) 29 MR2232855
7	I A Dynnikov, Transverse-Legendrian links, Sib. Èlektron. Mat. Izv. 16 (2019) 1960 MR4050236
8	I A Dynnikov, M V Prasolov, Bypasses for rectangular diagrams : a proof of the Jones conjecture and related questions, Trans. Moscow Math. Soc. (2013) 97 MR3235791
9	I A Dynnikov, M V Prasolov, Rectangular diagrams of surfaces: representability, Mat. Sb. 208 (2017) 55 MR3659579
10	I Dynnikov, M Prasolov, Rectangular diagrams of surfaces : distinguishing Legendrian knots, J. Topol. 14 (2021) 701 MR4286839
11	I A Dynnikov, V A Shastin, On the equivalence of Legendrian knots, Uspekhi Mat. Nauk 73 (2018) 195 MR3881792
12	I Dynnikov, V Shastin, Distinguishing Legendrian knots with trivial orientation-preserving symmetry group, preprint (2021) arXiv:1810.06460v3
13	Y Eliashberg, Invariants in contact topology, from: "Proceedings of the International Congress of Mathematicians, II" (editors G Fischer, U Rehmann), Deutsche Math. Vereinigung (1998) 327 MR1648083
14	Y Eliashberg, M Fraser, Classification of topologically trivial Legendrian knots, from: "Geometry, topology, and dynamics" (editor F Lalonde), CRM Proc. Lecture Notes 15, Amer. Math. Soc. (1998) 17 MR1619122
15	Y Eliashberg, M Fraser, Topologically trivial Legendrian knots, J. Symplectic Geom. 7 (2009) 77 MR2496415
16	J B Etnyre, K Honda, Knots and contact geometry, I : Torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001) 63 MR1959579
17	J B Etnyre, D J LaFountain, B Tosun, Legendrian and transverse cables of positive torus knots, Geom. Topol. 16 (2012) 1639 MR2967060
18	J B Etnyre, L L Ng, V Vértesi, Legendrian and transverse twist knots, J. Eur. Math. Soc. 15 (2013) 969 MR3085098
19	J Etnyre, V Vértesi, Legendrian satellites, Int. Math. Res. Not. 2018 (2018) 7241 MR3883132
20	D Fuchs, Chekanov–Eliashberg invariant of Legendrian knots : existence of augmentations, J. Geom. Phys. 47 (2003) 43 MR1985483
21	D Fuchs, S Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997) 1025 MR1445553
22	H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
23	P Ghiggini, Linear Legendrian curves in T³, Math. Proc. Cambridge Philos. Soc. 140 (2006) 451 MR2225643
24	E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637 MR1129802
25	E Giroux, Structures de contact en dimension trois et bifurcations des feuilletages de surfaces, Invent. Math. 141 (2000) 615 MR1779622
26	E Giroux, Structures de contact sur les variétés fibrées en cercles audessus d’une surface, Comment. Math. Helv. 76 (2001) 218 MR1839346
27	G D Gospodinov, Relative knot invariants: properties and applications, preprint (2009) arXiv:0909.4326
28	R Hartley, Knots with free period, Canadian J. Math. 33 (1981) 91 MR608857
29	S R Henry, J R Weeks, Symmetry groups of hyperbolic knots and links, J. Knot Theory Ramifications 1 (1992) 185 MR1164115
30	K Kodama, M Sakuma, Symmetry groups of prime knots up to 10 crossings, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 323 MR1177431
31	U Lüdicke, Zyklische Knoten, Arch. Math. (Basel) 32 (1979) 588 MR550326
32	C Manolescu, P Ozsváth, S Sarkar, A combinatorial description of knot Floer homology, Ann. of Math. 169 (2009) 633 MR2480614
33	J M Montesinos, Variedades de Seifert que son recubridores ciclicos ramificados de dos hojas, Bol. Soc. Mat. Mexicana 18 (1973) 1 MR341467
34	K Murasugi, On periodic knots, Comment. Math. Helv. 46 (1971) 162 MR292060
35	L L Ng, Computable Legendrian invariants, Topology 42 (2003) 55 MR1928645
36	L Ng, Combinatorial knot contact homology and transverse knots, Adv. Math. 227 (2011) 2189 MR2807087
37	P Ozsváth, Z Szabó, D Thurston, Legendrian knots, transverse knots and combinatorial Floer homology, Geom. Topol. 12 (2008) 941 MR2403802
38	P E Pushkar’, Y V Chekanov, Combinatorics of fronts of Legendrian links, and Arnol’d’s 4–conjectures, Uspekhi Mat. Nauk 60 (2005) 99 MR2145660
39	D Rolfsen, Knots and links, 7, Publish or Perish (1976) MR0515288
40	M Sakuma, The geometries of spherical Montesinos links, Kobe J. Math. 7 (1990) 167 MR1096689