Translation numbers for bundle automorphisms and a cocycle on a group of homeomorphisms

Abstract

We introduce and study translation numbers for automorphisms of principal $\mathbb{Z}$-bundles and flat principal $\mathbb{R}$-bundles. We use them to show a vanishing result of a characteristic class of foliated bundles and to detect undistortion elements in the group of bundle automorphisms.

arXiv comment15 pages, no figure