Seiberg–Witten–Floer stable homotopy type of three-manifolds with b1 = 0

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

Mathematical Subject Classification 2000

Primary: 57R58

Secondary: 57R57

References

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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

Volume 7, issue 2 (2003)

Ciprian Manolescu