Cost vs. integral foliated simplicial volume

TL;DR

This paper establishes a relationship between the integral foliated simplicial volume of closed manifolds and the cost of their fundamental groups, providing a new way to bound group invariants using geometric topology.

Contribution

It introduces a novel connection between integral foliated simplicial volume and the cost of groups, offering a new method to estimate group invariants from geometric data.

Findings

Integral foliated simplicial volume bounds the cost of fundamental groups.

Provides a new geometric approach to estimate group invariants.

Establishes a link between topology and group theory.

Abstract

We show that integral foliated simplicial volume of closed manifolds gives an upper bound for the cost of the corresponding fundamental groups.