Volume 18, issue 2 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2509–3131
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Stable presentation length of $3$–manifold groups

Ken’ichi Yoshida

Algebraic & Geometric Topology 18 (2018) 687–722
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