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Article overview
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A flexible construction of equivariant Floer homology and applications | | Kristen Hendricks
; Robert Lipshitz
; Sucharit Sarkar
; | | Date: |
8 Oct 2015 | | 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,
Ozsv’ath-Szab’o, Lipshitz-Treumann, Szab’o, Sarkar-Seed-Szab’o, 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-Szab’o’s; and
introduce a new concordance homomorphism and concordance invariants. We also
digress to prove invariance of Manolescu’s reduced symplectic Khovanov
homology. | | Source: | arXiv, 1510.2449 | | Services: | Forum | Review | PDF | Favorites | |
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