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Systolic volume of homology classes

Ivan Babenko and Florent Balacheff

Algebraic & Geometric Topology 15 (2015) 733–767
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