2015/10/31 by Kristen Hendricks, Robert Lipshitz, Sucharit Sarkar
Mathematics · #Advanced Combinatorial Mathematics #Cohomology #Equivariant map #Floer homology #Geometric and Algebraic Topology #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Spectral sequence #Symplectic geometry #math.GT #math.SG #msc:53D40 #msc:57M27 #msc:57R58
paper · pdf · doi:10.1112/jtopol/jtw022
published as J. Topol. 9 (2016), no. 4, 1153-1236 · 90 pages, 18 figures. V2: corrections and improvements thanks to referees. Similar to published version
openalex created_date 2016/06/24 · openalex publication_date 2016/10/20 · arxiv created 2017/04/16 · arxiv updated 2017/05/17 · openalex updated_date 2026/08/05
Seidel–Smith and Hendricks used equivariant Floer cohomology to define some spectral sequences from symplectic Khovanov homology and Heegaard Floer homology. These spectral sequences give rise to Smith-type inequalities. Similar-looking spectral sequences have been defined by Lee, Bar–Natan, Ozsváth–Szabó, Lipshitz–Treumann, Szabó, Sarkar–Seed–Szabó, and others. In this paper, we give another construction of equivariant Floer cohomology with respect to a finite group action and use it to prove some invariance properties of these spectral sequences; prove that some of these spectral sequences agree; improve Hendricks's Smith-type inequalities; give some theoretical and practical computability results for these spectral sequences; define some new spectral sequences conjecturally related to Sarkar–Seed–Szabó's; and introduce a new concordance homomorphism and concordance invariants. We also digress to prove invariance of Manolescu's reduced symplectic Khovanov homology.