Algebraic & Geometric Topology Volume 23, issue 5 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Adequate links in thickened surfaces and the generalized Tait conjectures

Hans U Boden, Homayun Karimi and Adam S Sikora

Algebraic & Geometric Topology 23 (2023) 2271–2308

DOI: 10.2140/agt.2023.23.2271

Bibliography

1	C Adams, C Albors-Riera, B Haddock, Z Li, D Nishida, B Reinoso, L Wang, Hyperbolicity of links in thickened surfaces, Topology Appl. 256 (2019) 262 MR3916014
2	C Adams, O Eisenberg, J Greenberg, K Kapoor, Z Liang, K O’Connor, N Pachecho-Tallaj, Y Wang, Turaev hyperbolicity of classical and virtual knots, Algebr. Geom. Topol. 21 (2021) 3459 MR4357610
3	C Adams, T Fleming, M Levin, A M Turner, Crossing number of alternating knots in S × I, Pacific J. Math. 203 (2002) 1 MR1895923
4	B Bavier, E Kalfagianni, Guts, volume and skein modules of 3–manifolds, Fund. Math. 256 (2022) 195 MR4361590
5	R C Blair, Alternating augmentations of links, J. Knot Theory Ramifications 18 (2009) 67 MR2490017
6	R Blair, H Allen, L Rodriguez, Twist number and the alternating volume of knots, J. Knot Theory Ramifications 28 (2019) MR3910957
7	C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
8	H U Boden, H Karimi, The Jones–Krushkal polynomial and minimal diagrams of surface links, Ann. Inst. Fourier (Grenoble) 72 (2022) 1437 MR4485830
9	H U Boden, H Karimi, A characterization of alternating links in thickened surfaces, Proc. Roy. Soc. Edinburgh Sect. A 153 (2023) 177 MR4546798
10	H U Boden, W Rushworth, Minimal crossing number implies minimal supporting genus, Bull. Lond. Math. Soc. 53 (2021) 1174 MR4311827
11	F Bonahon, H Wong, Quantum traces for representations of surface groups in SL₂(ℂ), Geom. Topol. 15 (2011) 1569 MR2851072
12	D Bullock, Rings of SL₂(ℂ)–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
13	D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265 MR1691437
14	J S Carter, S Kamada, M Saito, Stable equivalence of knots on surfaces and virtual knot cobordisms, J. Knot Theory Ramifications 11 (2002) 311 MR1905687
15	A Champanerkar, I Kofman, A survey on the Turaev genus of knots, Acta Math. Vietnam. 39 (2014) 497 MR3292579
16	A Champanerkar, I Kofman, A volumish theorem for alternating virtual links, New York J. Math. 28 (2022) 337 MR4381828
17	F Costantino, T T Q Lê, Stated skein algebras of surfaces, J. Eur. Math. Soc. 24 (2022) 4063 MR4493620
18	O T Dasbach, D Futer, E Kalfagianni, X S Lin, N W Stoltzfus, The Jones polynomial and graphs on surfaces, J. Combin. Theory Ser. B 98 (2008) 384 MR2389605
19	O T Dasbach, X S Lin, A volumish theorem for the Jones polynomial of alternating knots, Pacific J. Math. 231 (2007) 279 MR2346497
20	Y Diao, The additivity of crossing numbers, J. Knot Theory Ramifications 13 (2004) 857 MR2101230
21	H A Dye, L H Kauffman, Minimal surface representations of virtual knots and links, Algebr. Geom. Topol. 5 (2005) 509 MR2153118
22	V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
23	S Fomin, M Shapiro, D Thurston, Cluster algebras and triangulated surfaces, I : Cluster complexes, Acta Math. 201 (2008) 83 MR2448067
24	C Frohman, R Gelca, W Lofaro, The A–polynomial from the noncommutative viewpoint, Trans. Amer. Math. Soc. 354 (2002) 735 MR1862565
25	C Frohman, J Kania-Bartoszynska, T Lê, Unicity for representations of the Kauffman bracket skein algebra, Invent. Math. 215 (2019) 609 MR3910071
26	J A Howie, Surface-alternating knots and links, PhD thesis, University of Melbourne (2015)
27	J A Howie, J S Purcell, Geometry of alternating links on surfaces, Trans. Amer. Math. Soc. 373 (2020) 2349 MR4069222
28	N Kamada, On the Jones polynomials of checkerboard colorable virtual links, Osaka J. Math. 39 (2002) 325 MR1914297
29	N Kamada, S Kamada, Abstract link diagrams and virtual knots, J. Knot Theory Ramifications 9 (2000) 93 MR1749502
30	H Karimi, The Khovanov homology of alternating virtual links, Michigan Math. J. 70 (2021) 749 MR4332676
31	L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
32	V Krushkal, Graphs, links, and duality on surfaces, Combin. Probab. Comput. 20 (2011) 267 MR2769192
33	G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587 MR1997331
34	M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. 88 (2004) 204 MR2018964
35	M Lackenby, The crossing number of composite knots, J. Topol. 2 (2009) 747 MR2574742
36	T T Q Lê, The colored Jones polynomial and the A–polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
37	W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
38	W B R Lickorish, M B Thistlethwaite, Some links with nontrivial polynomials and their crossing-numbers, Comment. Math. Helv. 63 (1988) 527 MR966948
39	V O Manturov, Parity and projection from virtual knots to classical knots, J. Knot Theory Ramifications 22 (2013) MR3105303
40	W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
41	W Menasco, M Thistlethwaite, The classification of alternating links, Ann. of Math. 138 (1993) 113 MR1230928
42	G Muller, Skein and cluster algebras of marked surfaces, Quantum Topol. 7 (2016) 435 MR3551171
43	K Murasugi, Jones polynomials and classical conjectures in knot theory, Topology 26 (1987) 187 MR895570
44	J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45 MR1723531
45	J H Przytycki, A S Sikora, On skein algebras and Sl₂(ℂ)–character varieties, Topology 39 (2000) 115 MR1710996
46	A S Sikora, B W Westbury, Confluence theory for graphs, Algebr. Geom. Topol. 7 (2007) 439 MR2308953
47	R Stong, The Jones polynomial of parallels and applications to crossing number, Pacific J. Math. 164 (1994) 383 MR1272657
48	M B Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987) 297 MR899051
49	V G Turaev, A simple proof of the Murasugi and Kauffman theorems on alternating links, Enseign. Math. 33 (1987) 203 MR925987
50	V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov 167 (1988) 79 MR964255
51	V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906
52	V G Turaev, Algebras of loops on surfaces, algebras of knots, and quantization, from: "Braid group, knot theory and statistical mechanics, II" (editors C N Yang, M L Ge), Adv. Ser. Math. Phys. 17, World Sci. (1994) 324 MR1338608
53	D A Will, Homological polynomial coefficients and the twist number of alternating surface links, Algebr. Geom. Topol. 22 (2022) 3939 MR4562561