Systolic geometry and simplicial complexity for groups

Ivan Babenko (1) , Florent Balacheff (2) , Guillaume Bulteau (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 LPP - Laboratoire Paul Painlevé - UMR 8524

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.

Domaines: Mathématiques [math]

Ivan Babenko, Florent Balacheff, Guillaume Bulteau. Systolic geometry and simplicial complexity for groups. Journal für die reine und angewandte Mathematik, 2017, ⟨10.1515/crelle-2017-0041⟩. ⟨hal-02069192⟩