Poincaré's polyhedron theorem for cocompact groups in dimension 4

Details Poincaré's polyhedron theorem for cocompact groups in dimension 4 Poincaré's polyhedron theorem for cocompact groups in dimension 4

2011-12-24

arxiv.org/abs/1112.5740v1

Mathematics

Geometric Topology

14 pages, 1 figure, 10 references

Scientific paper

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 C-surfaces of general type satisfying c_1^2=3c_2.

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