Simplicial volume with $\mathbb{F}_p$-coefficients

TL;DR

This paper explores an $bF_p$-version of simplicial volume, compares it with other coefficients, and examines related gradient invariants and their relation to Betti numbers.

Contribution

It introduces an $bF_p$-version of simplicial volume and analyzes its properties and relations to Betti numbers and other coefficient-based invariants.

Findings

$bF_p$-simplicial volume differs from classical versions.

Gradient invariants stabilize along finite coverings.

Connections between simplicial volume and Betti numbers are established.

Abstract

For primes $p$, we investigate an $\mathbb{F}_p$-version of simplicial volume and compare these invariants with their siblings over other coefficient rings. We will also consider the associated gradient invariants, obtained by stabilisation along finite coverings. Throughout, we will discuss the relation between such simplicial volumes and Betti numbers.