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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Spinc–structures and homotopy equivalences

Robert E Gompf

Geometry & Topology 1 (1997) 41–50

DOI: 10.2140/gt.1997.1.41

arXiv: math.GT/9705218

Abstract

We show that a homotopy equivalence between manifolds induces a correspondence between their spinc–structures, even in the presence of 2–torsion. This is proved by generalizing spinc–structures to Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.

Keywords

4–manifold, Seiberg–Witten invariant, Poincaré complex

Mathematical Subject Classification

Primary: 57N13, 57R15

Secondary: 57P10, 57R19

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Publication

Received: 16 May 1997
Accepted: 17 October 1997
Published: 23 October 1997
Proposed: Ronald Stern
Seconded: Robion Kirby, Dieter Kotschick

Authors
Robert E Gompf
Department of Mathematics
The University of Texas at Austin
Austin
Texas 78712-1082
USA