Geometry & Topology Volume 24, issue 2 (2020)

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ISSN (electronic): 1364-0380

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Khovanov homotopy type, Burnside category and products

Tyler Lawson, Robert Lipshitz and Sucharit Sarkar

Geometry & Topology 24 (2020) 623–745

DOI: 10.2140/gt.2020.24.623

Bibliography

1	M Abouzaid, I Smith, Khovanov homology from Floer cohomology, J. Amer. Math. Soc. 32 (2019) 1 MR3867999
2	J F Adams, Stable homotopy and generalised homology, Univ. of Chicago Press (1974) MR0402720
3	J A Baldwin, W D Gillam, Computations of Heegaard–Floer knot homology, J. Knot Theory Ramifications 21 (2012) MR2925428
4	D Bar-Natan, Khovanov’s homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
5	D Bar-Natan, S Morrison, others, The knot atlas, online resource (2005)
6	J Bénabou, Introduction to bicategories, from: "Reports of the midwest category seminar" (editors A Dold, B Eckmann), Springer (1967) 1 MR0220789
7	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
8	S Cautis, J Kamnitzer, Knot homology via derived categories of coherent sheaves, I : The 𝔰𝔩(2)–case, Duke Math. J. 142 (2008) 511 MR2411561
9	R L Cohen, J D S Jones, G B Segal, Floer’s infinite-dimensional Morse theory and homotopy theory, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 297 MR1362832
10	J M Cordier, Sur la notion de diagramme homotopiquement cohérent, Cahiers Topologie Géom. Différentielle 23 (1982) 93 MR648798
11	W G Dwyer, D M Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980) 267 MR579087
12	A D Elmendorf, M A Mandell, Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006) 163 MR2254311
13	B Everitt, R Lipshitz, S Sarkar, P Turner, Khovanov homotopy types and the Dold–Thom functor, Homology Homotopy Appl. 18 (2016) 177 MR3547241
14	B Everitt, P Turner, The homotopy theory of Khovanov homology, Algebr. Geom. Topol. 14 (2014) 2747 MR3276847
15	O Flint, B Fontaine, R Furmaniak, S Rankin, Knotilus, software (2006)
16	A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
17	A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
18	A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
19	J W Gray, Formal category theory : adjointness for 2–categories, 391, Springer (1974) MR0371990
20	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
21	J Hom, Z Wu, Four-ball genus bounds and a refinement of the Ozváth–Szabó tau invariant, J. Symplectic Geom. 14 (2016) 305 MR3523259
22	P Hu, D Kriz, I Kriz, Field theories, stable homotopy theory, and Khovanov homology, Topology Proc. 48 (2016) 327 MR3465966
23	J R Isbell, On coherent algebras and strict algebras, J. Algebra 13 (1969) 299 MR249484
24	M Jacobsson, An invariant of link cobordisms from Khovanov homology, Algebr. Geom. Topol. 4 (2004) 1211 MR2113903
25	K Jänich, On the classification of O(n)–manifolds, Math. Ann. 176 (1968) 53 MR226674
26	M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
27	M Khovanov, Patterns in knot cohomology, I, Experiment. Math. 12 (2003) 365 MR2034399
28	M Khovanov, An invariant of tangle cobordisms, Trans. Amer. Math. Soc. 358 (2006) 315 MR2171235
29	M Khovanov, Link homology and Frobenius extensions, Fund. Math. 190 (2006) 179 MR2232858
30	G Laures, On cobordism of manifolds with corners, Trans. Amer. Math. Soc. 352 (2000) 5667 MR1781277
31	E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554 MR2173845
32	R D Leitch, The homotopy commutative cube, J. London Math. Soc. 9 (1974/75) 23 MR365560
33	T Lidman, C Manolescu, The equivalence of two Seiberg–Witten Floer homologies, 399, Soc. Math. France (2018) MR3818611
34	J Lin, Pin(2)–equivariant KO–theory and intersection forms of spin 4–manifolds, Algebr. Geom. Topol. 15 (2015) 863 MR3342679
35	R Lipshitz, S Sarkar, A Khovanov stable homotopy type, J. Amer. Math. Soc. 27 (2014) 983 MR3230817
36	R Lipshitz, S Sarkar, A refinement of Rasmussen’s S–invariant, Duke Math. J. 163 (2014) 923 MR3189434
37	R Lipshitz, S Sarkar, A Steenrod square on Khovanov homology, J. Topol. 7 (2014) 817 MR3252965
38	C Livingston, A H Moore, Knotinfo: table of knot invariants, online resource (2019)
39	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
40	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
41	C Manolescu, Seiberg–Witten–Floer stable homotopy type of three-manifolds with b₁ = 0, Geom. Topol. 7 (2003) 889 MR2026550
42	C Manolescu, On the intersection forms of spin four-manifolds with boundary, Math. Ann. 359 (2014) 695 MR3231012
43	G Naot, The universal Khovanov link homology theory, Algebr. Geom. Topol. 6 (2006) 1863 MR2263052
44	S Ovchinnikov, Geometric representations of weak orders, from: "Uncertainty and intelligent information systems" (editors B Bouchon-Meunier, C Marsala, M Rifqi, R R Yager), World Sci. (2008) 447
45	P Ozsváth, J Rasmussen, Z Szabó, Odd Khovanov homology, preprint (2007) arXiv:0710.4300
46	F Quinn, Lectures on axiomatic topological quantum field theory, from: "Geometry and quantum field theory" (editors D S Freed, K K Uhlenbeck), IAS/Park City Math. Ser. 1, Amer. Math. Soc. (1995) 323 MR1338394
47	J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) arXiv:math/0306378 MR2704683
48	J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
49	C Seed, Computations of the Lipshitz–Sarkar Steenrod square on Khovanov homology, preprint (2012) arXiv:1210.1882
50	C Seed, Knotkit, software (2014)
51	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
52	P Seidel, I Smith, A link invariant from the symplectic geometry of nilpotent slices, Duke Math. J. 134 (2006) 453 MR2254624
53	A N Shumakovitch, Patterns in odd Khovanov homology, J. Knot Theory Ramifications 20 (2011) 203 MR2777025
54	R M Switzer, Algebraic topology: homotopy and homology, 212, Springer (1975) MR0385836
55	P R Turner, Calculating Bar–Natan’s characteristic two Khovanov homology, J. Knot Theory Ramifications 15 (2006) 1335 MR2286127
56	P Turner, Khovanov homology and diagonalizable Frobenius algebras, J. Knot Theory Ramifications 29 (2020) MR4079621
57	R M Vogt, Homotopy limits and colimits, Math. Z. 134 (1973) 11 MR331376
58	Y Wigderson, The Bar–Natan theory splits, J. Knot Theory Ramifications 25 (2016) MR3482492
59	G M Ziegler, Lectures on polytopes, 152, Springer (1995) MR1311028