Geometry & Topology, Vol. 1 (1997) Paper no. 4, pages 41-50.

Spin^c structures and homotopy equivalences

Robert E Gompf

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

Keywords. 4-manifold, Seiberg-Witten invariant, Poincare complex

AMS subject classification. Primary: 57N13, 57R15. Secondary: 57P10, 57R19

DOI: 10.2140/gt.1997.1.41

E-print: arXiv:math.GT/9705218

Submitted to GT on May 16, 1997. Paper accepted October, 17 1997.

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

Email: gompf@math.utexas.edu

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