Geometry & Topology Volume 25, issue 4 (2021)

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A refinement of Khovanov homology

Andrew Lobb and Liam Watson

Geometry & Topology 25 (2021) 1861–1917

DOI: 10.2140/gt.2021.25.1861

Bibliography

1	D Bar-Natan, Khovanov’s homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
2	J M Bloom, Odd Khovanov homology is mutation invariant, Math. Res. Lett. 17 (2010) 1 MR2592723
3	C Collari, P Lisca, On symmetric equivalence of symmetric union diagrams, preprint (2019) arXiv:1901.10270
4	O Couture, Khovanov homology for signed divides, Algebr. Geom. Topol. 9 (2009) 1987 MR2550464
5	R Hartley, Knots and involutions, Math. Z. 171 (1980) 175 MR570907
6	A E Hatcher, A proof of the Smale conjecture, Diff(S³) ≃ O(4), Ann. of Math. 117 (1983) 553 MR701256
7	M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
8	S Kojima, M Yamasaki, Some new invariants of links, Invent. Math. 54 (1979) 213 MR553219
9	A Lobb, The Kanenobu knots and Khovanov–Rozansky homology, Proc. Amer. Math. Soc. 142 (2014) 1447 MR3162264
10	J W Morgan, H Bass, editors, The Smith conjecture, 112, Academic (1984) MR758459
11	P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 MR2023281
12	P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
13	P Ozsváth, Z Szabó, Knot Floer homology, genus bounds, and mutation, Topology Appl. 141 (2004) 59 MR2058681
14	L Piccirillo, The Conway knot is not slice, Ann. of Math. 191 (2020) 581 MR4076631
15	J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) arXiv:math/0306378 MR2704683
16	J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
17	K Reidemeister, Knotentheorie, 1, Springer (1932)
18	R Riley, An elliptical path from parabolic representations to hyperbolic structures, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 99 MR547459
19	D Rolfsen, Knots and links, 7, Publish or Perish (1976) MR0515288
20	M Sakuma, On strongly invertible knots, from: "Algebraic and topological theories" (editors M Nagata, S Araki, A Hattori), Kinokuniya (1986) 176 MR1102258
21	O Schreier, Über die Gruppen A^aB^b = 1, Abh. Math. Sem. Univ. Hamburg 3 (1924) 167 MR3069424
22	M Snape, Homological invariants of strongly invertible knots, PhD thesis, University of Glasgow (2018)
23	W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
24	H F Trotter, Non-invertible knots exist, Topology 2 (1963) 275 MR158395
25	F Waldhausen, Über Involutionen der 3–Sphäre, Topology 8 (1969) 81 MR236916
26	L Watson, Knots with identical Khovanov homology, Algebr. Geom. Topol. 7 (2007) 1389 MR2350287
27	L Watson, Khovanov homology and the symmetry group of a knot, Adv. Math. 313 (2017) 915 MR3649241
28	S M Wehrli, Mutation invariance of Khovanov homology over 𝔽₂, Quantum Topol. 1 (2010) 111 MR2657645