A flexible construction of equivariant Floer homology and applications

Abstract

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.

90 pages, 18 figures. V2: corrections and improvements thanks to referees. Similar to published version

References in corpus (3)

• Involutive Heegaard Floer homology
• Hamiltonian handleslides for Heegaard Floer homology
• Equivariant split generation and mirror symmetry of special isogenous tori

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