# Projective bundle theorem in homology theories with Chern structure

### Alexander Nenashev

York University - Glendon College Department of Mathematics 2275 Bayview Av., Toronto ON Canada M4N 3M6

## Abstract

Panin and Smirnov deduced the existence of push-forwards, along projective morphisms, in a cohomology theory with cup products, from the assumption that the theory is endowed with an extra structure called orientation. A part of their work is a proof of the Projective Bundle Theorem in cohomology based on the assumption that we have the first Chern class for line bundles. In some examples we have to consider a pair of theories, cohomology and homology, related by a cap product. It would be useful to construct transfer maps (pull-backs) along projective morphisms in homology in such a situation under similar assumptions. In this note we perform the projective bundle theorem part of this project in homology.

## Cite this article

Alexander Nenashev, Projective bundle theorem in homology theories with Chern structure. Doc. Math. 9 (2004), pp. 487–497

DOI 10.4171/DM/175