English

Yet Another Poincare's Polyhedron Theorem

Geometric Topology 2011-08-01 v3

Abstract

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.

Keywords

Cite

@article{arxiv.0812.4161,
  title  = {Yet Another Poincare's Polyhedron Theorem},
  author = {Sasha Anan'in and Carlos H. Grossi},
  journal= {arXiv preprint arXiv:0812.4161},
  year   = {2011}
}

Comments

9 pages, 2 figures, 5 references. Final version

R2 v1 2026-06-21T11:54:51.674Z