Fragmentation norm and relative quasimorphisms

TL;DR

This paper demonstrates that manifolds with sufficiently complex fundamental groups can have measure-preserving homeomorphisms with positive stable fragmentation norms, highlighting a link between topological complexity and fragmentation properties.

Contribution

It introduces a new connection between the complexity of a manifold's fundamental group and the existence of measure-preserving homeomorphisms with positive stable fragmentation norms.

Findings

Manifolds with complex fundamental groups admit measure-preserving homeomorphisms with positive stable fragmentation norm.

The result links topological complexity to fragmentation norm properties.

Provides new insights into the structure of measure-preserving homeomorphisms.

Abstract

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.