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Equivariant Seiberg-Witten-Floer cohomology
- Source :
- Algebr. Geom. Topol. 24 (2024) 493-554
- Publication Year :
- 2021
-
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 $d_{G,c}(Y,\mathfrak{s})$ which are indexed by the group cohomology of $G$. These invariants satisfy a Froyshov-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.<br />Comment: 58 pages, minor corrections
Details
- Database :
- arXiv
- Journal :
- Algebr. Geom. Topol. 24 (2024) 493-554
- Publication Type :
- Report
- Accession number :
- edsarx.2108.06855
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/agt.2024.24.493