Distribution of the systolic volume of homology classes

Ivan K. Babenko (1) , Florent Balacheff (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LPP - Laboratoire Paul Painlevé - UMR 8524

Given a pair (G,a) where G is a finitely presentable group and a is an integer homology class of this group, Gromov defined in his article "Filling Riemannian manifolds" a new numerical invariant associated to this pair called systolic volume. Our goal is to propose a systematic study of systolic volume as a function of the two variables G and a. In particular we focus on the distribution of the values of the systolic volume on the real line.

Mots clés: nilmanifold; torsion; multiple of a class; homology of a group with integer coefficients; Heisenberg group; representability of a homology class; Systolic volume

Domaines: Géométrie différentielle [math.DG]

Ivan K. Babenko, Florent Balacheff. Distribution of the systolic volume of homology classes. Algebraic and Geometric Topology, 2015, 15 (2), pp.733-767. ⟨10.2140/agt.2015.15.733⟩. ⟨hal-00517319⟩