Equivariant Seiberg-Witten Floer Homology
Matilde Marcolli (MIT), Bai-Ling Wang (University of Adelaide)
TL;DR
This paper develops an equivariant version of Seiberg-Witten Floer homology, addressing technical challenges in moduli space compactification, obstruction bundles, and gluing theorems to establish topological invariance.
Contribution
It introduces a detailed construction of equivariant Seiberg-Witten Floer homology, including new techniques for moduli space analysis and invariance proof.
Findings
Established topological invariance of the equivariant Floer homology
Developed new gluing theorems for moduli space compactification
Analyzed the structure of obstruction bundles in the Floer setting
Abstract
This paper circulated previously in a draft version. Now, upon general request, it is about time to distribute the more detailed (and much longer) version. The main technical issues revolve around the fine structure of the compactification of the moduli spaces of flow lines and the obstruction bundle technique, with related gluing theorems, needed in the proof of the topological invariance of the equivariant version of the Floer homology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory