Yet Another Poincare's Polyhedron Theorem

Sasha Anan'in; Carlos H. Grossi

doi:10.1017/s0013091509001783

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arXiv · 0812.4161

Yet Another Poincare's Polyhedron Theorem

Sasha Anan'in·Carlos H. Grossi

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Abstract

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 nonconstant curvature. Most conditions of the theorem, being as local as possible, are easy to verify in practice.

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BibTeX RIS

Sasha Anan'in, Carlos H. Grossi. 2011-07-29. Yet Another Poincare's Polyhedron Theorem. https://doi.org/10.1017/s0013091509001783

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