Geometry & Topology
- Geom. Topol.
- Volume 7, Number 2 (2003), 889-932.
Seiberg–Witten–Floer stable homotopy type of three-manifolds with $b_1=0$
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 –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.
Geom. Topol., Volume 7, Number 2 (2003), 889-932.
Received: 2 May 2002
Accepted: 5 December 2003
First available in Project Euclid: 21 December 2017
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Manolescu, Ciprian. Seiberg–Witten–Floer stable homotopy type of three-manifolds with $b_1=0$. Geom. Topol. 7 (2003), no. 2, 889--932. doi:10.2140/gt.2003.7.889. https://projecteuclid.org/euclid.gt/1513883325