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arXiv · 1112.5740

Poincaré's polyhedron theorem for cocompact groups in dimension 4

Sasha Anan'in·Carlos H. Grossi·Júlio C. C. da Silva
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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 $\mathbb C$-surfaces of general type satisfying $c_1^2=3c_2$.

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Sasha Anan'in, Carlos H. Grossi, Júlio C. C. da Silva. 2013-10-26. Poincaré's polyhedron theorem for cocompact groups in dimension 4. https://doi.org/10.17323/1609-4514-2014-14-4-645-667

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