Equivariant lattice homology for Seifert homology 3-spheres

Abstract

We develop an $S^1\times {\mathbb{Z}}_p$-equivariant refinement of the lattice homotopy type for Seifert homology 3-spheres equipped with the Seifert ${\mathbb{Z}}_p$-action. We construct an equivariant comparison map to the $S^1\times {\mathbb{Z}}_p$-equivariant Seiberg--Witten Floer spectrum that becomes an $S^1$-equivariant stable homotopy equivalence after forgetting the ${\mathbb{Z}}_p$-action, yielding a combinatorial description of its Borel equivariant cohomology.

arXiv comment61 pages. Substantially revised and retitled. The claim about exotic diffeomorphisms surviving two stabilizations in earlier versions has been removed due to a gap in the homotopy coherent action argument. This version focuses on equivariant lattice homology