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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 1997
- DOI:
- 10.48550/arXiv.math/9705218
- arXiv:
- arXiv:math/9705218
- Bibcode:
- 1997math......5218G
- Keywords:
-
- Mathematics - Geometric Topology;
- 57N13;
- 57R15;
- 57P10;
- 57R19
- E-Print:
- 10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper4.abs.html