Bounds on Systoles and Homotopy Complexity
Group Theory
2024-07-18 v3
Abstract
We give an elementary proof of a weak variant of the homotopy type conjecture from [Gel04]. The proof relies on Belolipetskys estimate on the systole in terms of the volume which is a consequence of Prasads volume formula. In particular we extend the estimate established in [B20] for hyperbolic manifolds to general arithmetic manifolds.
Cite
@article{arxiv.2106.10677,
title = {Bounds on Systoles and Homotopy Complexity},
author = {Tsachik Gelander and Paul Vollrath},
journal= {arXiv preprint arXiv:2106.10677},
year = {2024}
}