Algebraic & Geometric Topology Volume 20, issue 2 (2020)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Other MSP Journals

The Reidemeister graph is a complete knot invariant

Agnese Barbensi and Daniele Celoria

Algebraic & Geometric Topology 20 (2020) 643–698

DOI: 10.2140/agt.2020.20.643

Bibliography

1	J W Alexander, G B Briggs, On types of knotted curves, Ann. of Math. 28 (1926/27) 562 MR1502807
2	V I Arnold, Plane curves, their invariants, perestroikas and classifications, from: "Singularities and bifurcations" (editor V I Arnold), Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 33 MR1310595
3	S Baader, Note on crossing changes, Q. J. Math. 57 (2006) 139 MR2237515
4	R Budney, Structure of Gordian graph of knots, MathOverflow post (2016)
5	A Coward, M Lackenby, An upper bound on Reidemeister moves, Amer. J. Math. 136 (2014) 1023 MR3245186
6	T Ekholm, L Ng, V Shende, A complete knot invariant from contact homology, Invent. Math. 211 (2018) 1149 MR3763406
7	E Flapan, Infinitely periodic knots, Canad. J. Math. 37 (1985) 17 MR777036
8	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
9	R Halin, Über die Maximalzahl fremder unendlicher Wege in Graphen, Math. Nachr. 30 (1965) 63 MR190031
10	J Hass, T Nowik, Invariants of knot diagrams, Math. Ann. 342 (2008) 125 MR2415317
11	D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
12	L H Kauffman, S Lambropoulou, Hard unknots and collapsing tangles, from: "Introductory lectures on knot theory" (editors L H Kauffman, S Lambropoulou, S Jablan, J H Przytycki), Ser. Knots Everything 46, World Sci. (2012) 187 MR2885236
13	R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 273 MR520548
14	J Marché, Comportement à l’infini du graphe gordien des nœuds, C. R. Math. Acad. Sci. Paris 340 (2005) 363 MR2127111
15	Y Miyazawa, A distance for diagrams of a knot, Topology Appl. 159 (2012) 1122 MR2876719
16	M Polyak, Minimal generating sets of Reidemeister moves, Quantum Topol. 1 (2010) 399 MR2733246
17	K Reidemeister, Elementare Begründung der Knotentheorie, Abh. Math. Sem. Univ. Hamburg 5 (1927) 24 MR3069462
18	V A Vassiliev, Cohomology of knot spaces, from: "Theory of singularities and its applications" (editor V I Arnold), Adv. Soviet Math. 1, Amer. Math. Soc. (1990) 23 MR1089670