Geometry & Topology

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

Ciprian Manolescu

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.

Article information

Source
Geom. Topol., Volume 7, Number 2 (2003), 889-932.

Dates
Accepted: 5 December 2003
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883325

Digital Object Identifier
doi:10.2140/gt.2003.7.889

Mathematical Reviews number (MathSciNet)
MR2026550

Zentralblatt MATH identifier
1127.57303

Citation

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

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