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Yet another Poincaré Polyhedron Theorem

Part of: Lie groups Topological geometry Real and complex geometry

Published online by Cambridge University Press:  07 April 2011

Sasha Anan'in  and
Carlos H. Grossi
Sasha Anan'in
Affiliation:
Departamento de Matemática, IMECC, Universidade Estadual de Campinas, 13083-970-Campinas-SP, Brasil (ananin [email protected])
Carlos H. Grossi
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany ([email protected])
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Abstract

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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.

Keywords

Poincaré's Polyhedron Theoremdiscrete groupsgeometric structuresfibre bundles

MSC classification

Secondary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations 22E40: Discrete subgroups of Lie groups 51H05: General theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 297 - 308
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

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