Spin^c structures and homotopy equivalences

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.

10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper4.abs.html

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