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poincaré's polyhedron theorem

Proceedings of the Edinburgh Mathematical Society (1)

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Yet another Poincaré Polyhedron Theorem
Part of
Sasha Anan'in, Carlos H. Grossi
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 2 / June 2011

Published online by Cambridge University Press:

07 April 2011, pp. 297-308
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Poincaré's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a version of Poincaré's Polyhedron Theorem that is applicable to constructing fibre bundles over surfaces and also suits geometries of non-constant curvature. Most conditions of the theorem, being as local as possible, are easy to verify in practice.