Variants of equivariant Seiberg-Witten Floer homology

Details Variants of equivariant Seiberg-Witten Floer homology Variants of equivariant Seiberg-Witten Floer homology

2002-11-15

arxiv.org/abs/math/0211238v1

Mathematics

Geometric Topology

LaTeX 18 pages

Scientific paper

For a rational homology 3-sphere $Y$ with a $\spinc$ structure $\s$, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology lead to a collection of variants which are topological invariants. We establish exact sequences relating them, we show that they satisfy a duality under orientation reversal, and we explain their relation to ou previous construction of equivariant Seiberg-Witten Floer (co)homologies. We conjecture the equivalence of these versions of equivariant Seiberg-Witten Floer homology with the Heegaard Floer invariants introduced by Ozsv\'ath and Szab\'o.

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