Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0

Details Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0 Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0

2001-04-02

arxiv.org/abs/math/0104024v3

Geom. Topol. 7(2003) 889-932

Mathematics

Differential Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper26.abs.html

Scientific paper

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.

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