Integral foliated simplicial volume and circle foliations

TL;DR

This paper proves that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a circle foliation is zero, revealing a significant property of such foliated manifolds.

Contribution

It establishes the vanishing of integral foliated simplicial volume for manifolds with circle foliations, a novel result in the study of foliated manifold invariants.

Findings

Integral foliated simplicial volume of such manifolds vanishes

Provides new insights into the topology of circle foliated manifolds

Enhances understanding of foliated manifold invariants

Abstract

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.