### Projective bundle theorem in homology theories with Chern structure, by Alexander Nenashev

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.

A very recent preprint by K. Pimenov (0667) contains a proof of the same
theorem. However, the general framework in which he considers a homology theory
and the way he proves it are somewhat different from mines. (See more comments
on these differences in the introduction.)

Alexander Nenashev <nenashev@math.uregina.ca>