Equivariant Seiberg–Witten–Floer cohomology

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; 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.