Simplicial volume of manifolds fibering with connected structure group

TL;DR

This paper studies how the simplicial volume of fiber bundles behaves when the structure group is connected, showing it matches the trivial bundle's volume under certain conditions.

Contribution

It proves that the simplicial volume of fiber bundles with connected structure group equals that of the trivial bundle when the group is compact, a Lie group, or the fiber is aspherical.

Findings

Simplicial volume equals that of the trivial bundle under specified conditions.

Connected structure groups like compact or Lie groups preserve simplicial volume.

Aspherical fibers lead to the same simplicial volume as trivial bundles.

Abstract

In this note we investigate the simplicial volume of fiber bundles with connected structure group. We are able to show that if the structure group is either compact or a Lie group, or if the fiber is aspherical that the simplicial volume of the total space agrees with the simplicial volume of the trivial bundle.