Rank gradient vs. stable integral simplicial volume

TL;DR

This paper establishes a relationship between the stable integral simplicial volume of closed manifolds and the rank gradient of their fundamental groups, providing a new way to bound algebraic invariants using geometric measures.

Contribution

It introduces a novel upper bound for the rank gradient based on the stable integral simplicial volume, linking geometric and algebraic properties of manifolds.

Findings

Stable integral simplicial volume bounds the rank gradient from above.

Provides a new geometric approach to estimate algebraic invariants.

Establishes a connection between topology and group theory in manifold studies.

Abstract

We observe that stable integral simplicial volume of closed manifolds gives an upper bound for the rank gradient of the corresponding fundamental groups.