Stable presentation length of 3–manifold groups

Yoshida, Ken’ichi

doi:10.2140/agt.2018.18.687

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Stable presentation length of $3$–manifold groups

Ken’ichi Yoshida

Algebraic & Geometric Topology 18 (2018) 687–722

DOI: 10.2140/agt.2018.18.687

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.

Keywords

presentations of groups, finite covers of 3-manifolds

Mathematical Subject Classification 2010

Primary: 57M05, 57M27

Secondary: 57M10, 57M20

References

Publication

Received: 23 September 2015

Revised: 15 September 2017

Accepted: 8 October 2017

Published: 12 March 2018

Authors

Ken’ichi Yoshida
Department of Mathematics Kyoto University Kyoto Japan

Volume 18, issue 2 (2018)