Integral foliated simplicial volume and circle foliations

Abstract

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

Multiplicative constants and maximal measurable cocycles in bounded cohomology

“…In the literature about the ergodic version of simplicial volume [CC21, FFL19, FFM12, FLMQ21, FLPS16, LP16, Sau02, Sch05], it is often convenient to work with essentially free actions. For this reason, one might find it reasonable to stick with the same assumptions also here working with the dual notion of bounded cohomology.…”