Poincar\'e's polyhedron theorem for cocompact groups in dimension 4
Geometric Topology
2020-01-27 v2
Abstract
We prove a version of Poincar\'e's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can be generalized to the case of higher dimension and other geometric structures. It is planned as a first step in a program of constructing compact -surfaces of general type satisfying .
Cite
@article{arxiv.1112.5740,
title = {Poincar\'e's polyhedron theorem for cocompact groups in dimension 4},
author = {Sasha Anan'in and Carlos H. Grossi and Júlio C. C. da Silva},
journal= {arXiv preprint arXiv:1112.5740},
year = {2020}
}
Comments
15 pages, 1 figure, 9 references. Introduction revised. Example 3.16 added