Systolic geometry and simplicial complexity for groups
Geometric Topology
2023-04-03 v2 Differential Geometry
Group Theory
Abstract
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 {\it 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.
Cite
@article{arxiv.1501.01173,
title = {Systolic geometry and simplicial complexity for groups},
author = {Ivan Babenko and Florent Balacheff and Guillaume Bulteau},
journal= {arXiv preprint arXiv:1501.01173},
year = {2023}
}
Comments
35 pages, 9 figures