Stable presentation length of 3-manifold groups

TL;DR

This paper introduces the stable presentation length for finitely presented groups, especially fundamental groups of 3-manifolds, showing it shares properties with simplicial volume and relates closely to the manifold's geometric invariants.

Contribution

It defines the stable presentation length for 3-manifold groups and establishes its additive properties and bounds in relation to simplicial volume.

Findings

Stable presentation length is introduced for finitely presented groups.

It exhibits additive properties similar to simplicial volume.

Bounds relate simplicial volume and stable presentation length of 3-manifolds.

Abstract

We introduce the stable presentation length of a finitely presented group. The stable presentation length of the fundamental group of a 3-manifold can be considered as an analogue of the simplicial volume. We show that the stable presentation length have some additive properties like the simplicial volume, and the simplicial volume of a closed 3-manifold is bounded from above and below by constant multiples of the stable presentation length of its fundamental group.