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 <>