#### Volume 7, issue 2 (2003)

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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 ${S}^{1}$–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
Primary: 57R58
Secondary: 57R57