Geometry & Topology

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

Ciprian Manolescu

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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

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R58: Floer homology
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

3–manifolds Floer homology Seiberg–Witten equations Bauer–Furuta invariant Conley index


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.

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