Yet Another Poincare's Polyhedron Theorem

Details Yet Another Poincare's Polyhedron Theorem Yet Another Poincare's Polyhedron Theorem

2008-12-22

arxiv.org/abs/0812.4161v3

Proceedings of the Edinburgh Mathematical Society, Volume 54 (2011), Issue 2, pp. 297--308

Mathematics

Geometric Topology

9 pages, 2 figures, 5 references. Final version

Scientific paper

10.1017/S0013091509001783

Poincar\'e'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 Poincar\'e'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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