Revisiting Poincar\'e's Theorem on presentations of discontinuous groups via fundamental polyhedra
Group Theory
2015-04-30 v1
Abstract
We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only makes use of basic geometric concepts. In a sense one hence obtains a proof that is of a more constructive nature than most known proofs.
Keywords
Cite
@article{arxiv.1504.07779,
title = {Revisiting Poincar\'e's Theorem on presentations of discontinuous groups via fundamental polyhedra},
author = {Eric Jespers and Ann Kiefer and Ángel del Río},
journal= {arXiv preprint arXiv:1504.07779},
year = {2015}
}
Comments
38 pages