Equivariant Seiberg-Witten-Floer cohomology
Date
2024
Authors
Baraglia, D.
Hekmati, P.
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Journal article
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Algebraic and Geometric Topology, 2024; 24(1):493-554
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David Baraglia, Pedram Hekmati
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Abstract
We develop an equivariant version of Seiberg–Witten–Floer cohomology for finite group actions on rational homology 3–spheres. Our construction is based on an equivariant version of the Seiberg–Witten– Floer stable homotopy type, as constructed by Manolescu. We use these equivariant cohomology groups to define a series of d–invariants d<inf>G,c</inf> (Y, s) which are indexed by the group cohomology of G. These invariants satisfy a Frøyshov-type inequality under equivariant cobordisms. Lastly, we consider a variety of applications of these d–invariants: concordance invariants of knots via branched covers, obstructions to extending group actions over bounding 4–manifolds, Nielsen realisation problems for 4–manifolds with boundary and obstructions to equivariant embeddings of 3–manifolds in 4–manifolds.
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© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).