Cohomology of preimages with local coefficients
Geometric Topology
2009-04-28 v1 Algebraic Topology
Abstract
Let M,N and B\subset N be compact smooth manifolds of dimensions n+k,n and \ell, respectively. Given a map f from M to N, we give homological conditions under which g^{-1}(B) has nontrivial cohomology (with local coefficients) for any map g homotopic to f. We also show that a certain cohomology class in H^j(N,N-B) is Poincare dual (with local coefficients) under f^* to the image of a corresponding class in H_{n+k-j}(f^{-1}(B)) when f is transverse to B. This generalizes a similar formula of D Gottlieb in the case of simple coefficients.
Cite
@article{arxiv.0904.4177,
title = {Cohomology of preimages with local coefficients},
author = {Daciberg Lima Goncalves and Peter Wong},
journal= {arXiv preprint arXiv:0904.4177},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 4 October 2006