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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Seiberg–Witten–Floer stable homotopy type of three-manifolds with $b_1=0$

Ciprian Manolescu

Geometry & Topology 7 (2003) 889–932

arXiv: math.DG/0104024

Abstract

Using Furuta’s idea of finite dimensional approximation in Seiberg–Witten theory, we refine Seiberg–Witten Floer homology to obtain an invariant of homology 3–spheres which lives in the S1–equivariant graded suspension category. In particular, this gives a construction of Seiberg–Witten Floer homology that avoids the delicate transversality problems in the standard approach. We also define a relative invariant of four-manifolds with boundary which generalizes the Bauer–Furuta stable homotopy invariant of closed four-manifolds.

Keywords
3–manifolds, Floer homology, Seiberg–Witten equations, Bauer–Furuta invariant, Conley index
Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 57R57
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Publication
Received: 2 May 2002
Accepted: 5 December 2003
Published: 10 December 2003
Proposed: Tomasz Mrowka
Seconded: Dieter Kotschick, Ralph Cohen
Authors
Ciprian Manolescu
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge
Massachusetts 02138
USA