Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Localization in Khovanov homology

Matthew Stoffregen and Melissa Zhang

Geometry & Topology 28 (2024) 1501–1585
Bibliography
1 M Abouzaid, I Smith, Khovanov homology from Floer cohomology, J. Amer. Math. Soc. 32 (2019) 1 MR3867999
2 J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR0764596
3 R Akhmechet, V Krushkal, M Willis, Stable homotopy refinement of quantum annular homology, Compos. Math. 157 (2021) 710 MR4247571
4 R Akhmechet, V Krushkal, M Willis, Towards an 𝔰𝔩2 action on the annular Khovanov spectrum, Adv. Math. 408 (2022) 108581 MR4456790
5 M M Asaeda, J H Przytycki, A S Sikora, Categorification of the skein module of tangles, from: "Primes and knots" (editors T Kohno, M Morishita), Contemp. Math. 416, Amer. Math. Soc. (2006) 1 MR2276132
6 D Auroux, J E Grigsby, S M Wehrli, Sutured Khovanov homology, Hochschild homology, and the Ozsváth–Szabó spectral sequence, Trans. Amer. Math. Soc. 367 (2015) 7103 MR3378825
7 D Bar-Natan, On Khovanov’s categorification of the Jones polynomial, Algebr. Geom. Topol. 2 (2002) 337 MR1917056
8 D Bar-Natan, Khovanov’s homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
9 A Beliakova, K K Putyra, S M Wehrli, Quantum link homology via trace functor, I, Invent. Math. 215 (2019) 383 MR3910068
10 J Bénabou, Introduction to bicategories, from: "Reports of the Midwest category seminar" (editors A Dold, B Eckmann), Lecture Notes in Math. 47, Springer (1967) 1 MR0220789
11 M Borodzik, W Politarczyk, M Silvero, Khovanov homotopy type, periodic links and localizations, Math. Ann. 380 (2021) 1233 MR4297186
12 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
13 K Boyle, Rank inequalities on knot Floer homology of periodic knots, Bull. Lond. Math. Soc. 54 (2022) 668 MR4453698
14 G E Bredon, Equivariant cohomology theories, Bull. Amer. Math. Soc. 73 (1967) 266 MR0206946
15 Y Chen, M Khovanov, An invariant of tangle cobordisms via subquotients of arc rings, Fund. Math. 225 (2014) 23 MR3205563
16 V Colin, P Ghiggini, K Honda, Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, Proc. Natl. Acad. Sci. USA 108 (2011) 8100 MR2806645
17 G Cooke, Replacing homotopy actions by topological actions, Trans. Amer. Math. Soc. 237 (1978) 391 MR0461544
18 S R Costenoble, J P May, S Waner, Equivariant orientation theory, Homology Homotopy Appl. 3 (2001) 265 MR1856029
19 S R Costenoble, S Waner, Equivariant ordinary homology and cohomology, 2178, Springer (2016) MR3585352
20 E Dotto, K Moi, Homotopy theory of G–diagrams and equivariant excision, Algebr. Geom. Topol. 16 (2016) 325 MR3470703
21 W G Dwyer, D M Kan, J H Smith, Homotopy commutative diagrams and their realizations, J. Pure Appl. Algebra 57 (1989) 5 MR0984042
22 J P C Greenlees, J P May, Equivariant stable homotopy theory, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 277 MR1361893
23 J E Grigsby, A M Licata, S M Wehrli, Annular Khovanov homology and knotted Schur–Weyl representations, Compos. Math. 154 (2018) 459 MR3731256
24 J E Grigsby, S M Wehrli, An action of 𝔤𝔩(1|1) on odd annular Khovanov homology, Math. Res. Lett. 27 (2020) 711 MR4216566
25 K Hendricks, A rank inequality for the knot Floer homology of double branched covers, Algebr. Geom. Topol. 12 (2012) 2127 MR3020203
26 K Hendricks, Localization of the link Floer homology of doubly-periodic knots, J. Symplectic Geom. 13 (2015) 545 MR3412087
27 K Hendricks, R Lipshitz, S Sarkar, A flexible construction of equivariant Floer homology and applications, J. Topol. 9 (2016) 1153 MR3620455
28 P Hu, D Kriz, I Kriz, Field theories, stable homotopy theory, and Khovanov homology, Topology Proc. 48 (2016) 327 MR3465966
29 S Illman, Smooth equivariant triangulations of G–manifolds for G a finite group, Math. Ann. 233 (1978) 199 MR0500993
30 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
31 M Khovanov, A functor-valued invariant of tangles, Algebr. Geom. Topol. 2 (2002) 665 MR1928174
32 M Khovanov, L Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 MR2391017
33 M Khovanov, L Rozansky, Matrix factorizations and link homology, II, Geom. Topol. 12 (2008) 1387 MR2421131
34 Ç Kutluhan, Y J Lee, C H Taubes, HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology, Geom. Topol. 24 (2020) 2829 MR4194305
35 T Large, Equivariant Floer theory and double covers of three-manifolds, preprint (2019) arXiv:1910.12119
36 A D Lauda, An introduction to diagrammatic algebra and categorified quantum 𝔰𝔩2, Bull. Inst. Math. Acad. Sin. 7 (2012) 165 MR3024893
37 T Lawson, R Lipshitz, S Sarkar, The cube and the Burnside category, from: "Categorification in geometry, topology, and physics" (editors A Beliakova, A D Lauda), Contemp. Math. 684, Amer. Math. Soc. (2017) 63 MR3611723
38 T Lawson, R Lipshitz, S Sarkar, Khovanov homotopy type, Burnside category and products, Geom. Topol. 24 (2020) 623 MR4153651
39 T Lawson, R Lipshitz, S Sarkar, Chen–Khovanov spectra for tangles, Michigan Math. J. 71 (2022) 401 MR4484244
40 T Lawson, R Lipshitz, S Sarkar, Khovanov spectra for tangles, J. Inst. Math. Jussieu 22 (2023) 1509 MR4611197
41 T Lidman, C Manolescu, The equivalence of two Seiberg–Witten Floer homologies, 399, Soc. Math. France (2018) MR3818611
42 T Lidman, C Manolescu, Floer homology and covering spaces, Geom. Topol. 22 (2018) 2817 MR3811772
43 R Lipshitz, S Sarkar, A Khovanov stable homotopy type, J. Amer. Math. Soc. 27 (2014) 983 MR3230817
44 R Lipshitz, D Treumann, Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers, J. Eur. Math. Soc. 18 (2016) 281 MR3459952
45 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
46 J Musyt, Equivariant Khovanov homotopy type and periodic links, PhD thesis, University of Oregon (2019) MR4035428
47 P S Ozsváth, J Rasmussen, Z Szabó, Odd Khovanov homology, Algebr. Geom. Topol. 13 (2013) 1465 MR3071132
48 W Politarczyk, Equivariant Khovanov homology of periodic links, Michigan Math. J. 68 (2019) 859 MR4029632
49 L P Roberts, On knot Floer homology in double branched covers, Geom. Topol. 17 (2013) 413 MR3035332
50 S Sarkar, C Scaduto, M Stoffregen, An odd Khovanov homotopy type, Adv. Math. 367 (2020) 107112 MR4078823
51 S Sarkar, C Seed, Z Szabó, A perturbation of the geometric spectral sequence in Khovanov homology, Quantum Topol. 8 (2017) 571 MR3692911
52 P Seidel, I Smith, A link invariant from the symplectic geometry of nilpotent slices, Duke Math. J. 134 (2006) 453 MR2254624
53 P Seidel, I Smith, Localization for involutions in Floer cohomology, Geom. Funct. Anal. 20 (2010) 1464 MR2739000
54 P A Smith, Transformations of finite period, Ann. of Math. 39 (1938) 127 MR1503393
55 C Stroppel, Categorification of the Temperley–Lieb category, tangles, and cobordisms via projective functors, Duke Math. J. 126 (2005) 547 MR2120117
56 R M Vogt, Homotopy limits and colimits, Math. Z. 134 (1973) 11 MR0331376
57 M Willis, Stabilization of the Khovanov homotopy type of torus links, Int. Math. Res. Not. 2017 (2017) 3350 MR3693652
58 Y Xie, Instantons and annular Khovanov homology, Adv. Math. 388 (2021) 107864 MR4281775
59 M Zhang, A rank inequality for the annular Khovanov homology of 2–periodic links, Algebr. Geom. Topol. 18 (2018) 1147 MR3773751