Geodesic
Equivariant Seiberg–Witten–Floer cohomology
Baraglia, David1 ; Hekmati, Pedram2
1 School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, Australia
2 Department of Mathematics, The University of Auckland, Auckland, New Zealand
Algebraic and Geometric Topology, Tome 24 (2024) no. 1, pp. 493-554

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 dG,c(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.

DOI : 10.2140/agt.2024.24.493
Keywords: Seiberg–Witten, Floer homology, Conley index, equivariant cohomology

Baraglia, David 1 ; Hekmati, Pedram 2

1 School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, Australia
2 Department of Mathematics, The University of Auckland, Auckland, New Zealand 
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Baraglia, David; Hekmati, Pedram. Equivariant Seiberg–Witten–Floer cohomology. Algebraic and Geometric Topology, Tome 24 (2024) no. 1, pp. 493-554. doi: 10.2140/agt.2024.24.493

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