Equivariant Seiberg-Witten-Floer cohomology
| Autor: | Baraglia, David, Hekmati, Pedram |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Algebr. Geom. Topol. 24 (2024) 493-554 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/agt.2024.24.493 |
| Popis: | 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. Comment: 58 pages, minor corrections |
| Databáze: | arXiv |
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