Systolic volume of homology classes

Babenko, Ivan; Balacheff, Florent

doi:10.2140/agt.2015.15.733

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Systolic volume of homology classes

Ivan Babenko and Florent Balacheff

Algebraic & Geometric Topology 15 (2015) 733–767

DOI: 10.2140/agt.2015.15.733

Abstract

Given an integer homology class of a finitely presentable group, the systolic volume quantifies how tight a geometric realization of this class could be. In this paper, we study various aspects of this numerical invariant showing that it is a complex and powerful tool for investigating topological properties of homology classes of finitely presentable groups.

Keywords

systolic volume, integer homology of a group, representability of a homology class

Mathematical Subject Classification 2010

Primary: 53C23

Secondary: 20J06, 20F99

References

Publication

Received: 12 November 2013

Revised: 10 July 2014

Accepted: 9 September 2014

Published: 22 April 2015

Authors

Ivan Babenko
Institut de Mathématiques et de Modélisation de Montpellier Université Montpellier 2 Case Courrier 051 Place Eugène Bataillon 34095 Montpellier Cedex France

Florent Balacheff
Laboratoire Paul Painlevé Université Lille 1 Bâtiment M2 Cité Scientifique 59655 Villeneuve-d’Ascq Cedex France

Volume 15, issue 2 (2015)