Stable presentation length of $3$–manifold groups

Abstract

We introduce the stable presentation length of a finitely presentable 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, like the simplicial volume, the stable presentation length has some additive properties, 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.