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 Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.