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.
Bibliographical noteAcknowledgments. We would like to thank Lev Buhovsky, Yaron Ostrover and Leonid Polterovich for helpful discussions. We would like to thank the referees for a thorough reading of our paper and for very useful suggestions.
We thank the Center for Advanced Studies in Mathematics at Ben Gurion University for supporting the visit of the second author at BGU. This work was funded by a Leverhulme Trust Research Project Grant RPG-2017-159.
- measure-preserving homeomorphisms
- Hamiltonian diffeomorphisms
- fragmentation norm
- relative quasimorphisms