Poincaré's polyhedron theorem for cocompact groups in dimension 4

Sasha Anan'in; Carlos H. Grossi; Júlio C. C. da Silva

doi:10.17323/1609-4514-2014-14-4-645-667

paper

Poincaré's polyhedron theorem for cocompact groups in dimension 4

arXiv:1112.5740 · doi:10.17323/1609-4514-2014-14-4-645-667

Abstract

We prove a version of Poincaré'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 $C$ -surfaces of general type satisfying $c_{1}^{2} = 3 c_{2}$ .

15 pages, 1 figure, 9 references. Introduction revised. Example 3.16 added