Year: 2025
Type: article
Abstract: Many concepts in differential geometry (for example, Riemannian metric, length, shortest arc, volume), defined originally for manifolds, are easily transferred to simplicial polyhedra. This extends significantly the scope of application of such concepts familiar in the framework of manifolds as systolic volume and volume entropy. Many properties of these invariants depend only on the fundamental group of the polyhedron. Using the process of minimisation, it becomes possible to transfer these invariants directly to finitely presented groups. In studying the systolic area and volume entropy of groups, new combinatorial invariants arise, which are of independent interest. The paper is an introduction to this area at the intersection of geometry, topology, and group theory. Bibliography: 65 titles.
Source: Russian Mathematical Surveys
DOI: 10.4213/rm10232e
Author: Ivan Konstantinovich Babenko
Institution: Université de Montpellier
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411497742