#### Geometry & Topology, Vol. 7 (2003)
Paper no. 26, pages 889--932.

## 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
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

**AMS subject classification**.
Primary: 57R58.
Secondary: 57R57.

**DOI:** 10.2140/gt.2003.7.889

**E-print:** `arXiv:math.DG/0104024`

Submitted to GT on 2 May 2002.
Paper accepted 5 December 2003.
Paper published 10 December 2003.

Notes on file formats
Ciprian Manolescu

Department of Mathematics, Harvard University

1 Oxford Street, Cambridge, MA 02138, USA

Email: manolesc@fas.harvard.edu

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**