Volume 18, issue 2 (2018)

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Stable presentation length of $3$–manifold groups

Ken’ichi Yoshida

Algebraic & Geometric Topology 18 (2018) 687–722

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.

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presentations of groups, finite covers of 3-manifolds
Mathematical Subject Classification 2010
Primary: 57M05, 57M27
Secondary: 57M10, 57M20
Received: 23 September 2015
Revised: 15 September 2017
Accepted: 8 October 2017
Published: 12 March 2018
Ken’ichi Yoshida
Department of Mathematics
Kyoto University