Algebraic & Geometric Topology Volume 19, issue 1 (2019)

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

Arrow calculus for welded and classical links

Jean-Baptiste Meilhan and Akira Yasuhara

Algebraic & Geometric Topology 19 (2019) 397–456

DOI: 10.2140/agt.2019.19.397

Bibliography

1	B Audoux, P Bellingeri, J B Meilhan, E Wagner, Homotopy classification of ribbon tubes and welded string links, Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (2017) 713 MR3700382
2	B Audoux, P Bellingeri, J B Meilhan, E Wagner, Extensions of some classical local moves on knot diagrams, Michigan Math. J. 67 (2018) 647 MR3835567
3	B Audoux, J B Meilhan, E Wagner, On codimension two embeddings up to link-homotopy, J. Topol. 10 (2017) 1107 MR3743070
4	D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications 4 (1995) 13 MR1321289
5	D Bar-Natan, Z Dancso, Finite-type invariants of w-knotted objects, I : w-knots and the Alexander polynomial, Algebr. Geom. Topol. 16 (2016) 1063 MR3493416
6	T E Brendle, A Hatcher, Configuration spaces of rings and wickets, Comment. Math. Helv. 88 (2013) 131 MR3008915
7	R Fenn, R Rimányi, C Rourke, The braid-permutation group, Topology 36 (1997) 123 MR1410467
8	T Fiedler, Gauss diagram invariants for knots and links, 532, Kluwer (2001) MR1948012
9	M Goussarov, M Polyak, O Viro, Finite-type invariants of classical and virtual knots, Topology 39 (2000) 1045 MR1763963
10	M Gusarov, On n–equivalence of knots and invariants of finite degree, from: "Topology of manifolds and varieties" (editor O Viro), Adv. Soviet Math. 18, Amer. Math. Soc. (1994) 173 MR1296895
11	N Habegger, X S Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990) 389 MR1026062
12	N Habegger, G Masbaum, The Kontsevich integral and Milnor’s invariants, Topology 39 (2000) 1253 MR1783857
13	K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
14	K Habiro, T Kanenobu, A Shima, Finite type invariants of ribbon 2–knots, from: "Low-dimensional topology" (editor H Nencka), Contemp. Math. 233, Amer. Math. Soc. (1999) 187 MR1701683
15	K Habiro, J B Meilhan, On the Kontsevich integral of Brunnian links, Algebr. Geom. Topol. 6 (2006) 1399 MR2253452
16	K Habiro, A Shima, Finite type invariants of ribbon 2–knots, II, Topology Appl. 111 (2001) 265 MR1814229
17	A Ichimori, T Kanenobu, Ribbon torus knots presented by virtual knots with up to four crossings, J. Knot Theory Ramifications 21 (2012) MR2994592
18	T Kanenobu, Virtual arc presentations and HC-moves of ribbon 2–knots, J. Knot Theory Ramifications 11 (2002) 387 MR1905693
19	T Kanenobu, A Shima, Two filtrations of ribbon 2–knots, Topology Appl. 121 (2002) 143 MR1903688
20	L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663 MR1721925
21	X S Lin, Power series expansions and invariants of links, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 184 MR1470727
22	J B Meilhan, A Yasuhara, On C_n–moves for links, Pacific J. Math. 238 (2008) 119 MR2443510
23	J B Meilhan, A Yasuhara, Characterization of finite type string link invariants of degree < 5, Math. Proc. Cambridge Philos. Soc. 148 (2010) 439 MR2609302
24	J Milnor, Link groups, Ann. of Math. 59 (1954) 177 MR0071020
25	J Milnor, Isotopy of links, from: "Algebraic geometry and topology : a symposium in honor of S Lefschetz" (editors R H Fox, D C Spencer, A W Tucker), Princeton Univ. Press (1957) 280 MR0092150
26	T Ohtsuki, Problems on invariants of knots and 3–manifolds, from: "Invariants of knots and 3–manifolds" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev), Geom. Topol. Monogr. 4, Geom. Topol. Publ. (2002) 377 MR2065029
27	M Polyak, On the algebra of arrow diagrams, Lett. Math. Phys. 51 (2000) 275 MR1778064
28	M Polyak, Minimal generating sets of Reidemeister moves, Quantum Topol. 1 (2010) 399 MR2733246
29	M Polyak, O Viro, Gauss diagram formulas for Vassiliev invariants, Int. Math. Res. Not. 1994 (1994) 445 MR1316972
30	S Satoh, Virtual knot presentation of ribbon torus-knots, J. Knot Theory Ramifications 9 (2000) 531 MR1758871
31	T Watanabe, Clasper-moves among ribbon 2–knots characterizing their finite type invariants, J. Knot Theory Ramifications 15 (2006) 1163 MR2287439
32	T Yajima, On the fundamental groups of knotted 2–manifolds in the 4–space, J. Math. Osaka City Univ. 13 (1962) 63 MR0151960
33	A Yasuhara, Self delta-equivalence for links whose Milnor’s isotopy invariants vanish, Trans. Amer. Math. Soc. 361 (2009) 4721 MR2506425