Yet Another Poincare's Polyhedron Theorem

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.

9 pages, 2 figures, 5 references. Final version

References in corpus (1)

• Complex Hyperbolic Structures on Disc Bundles over Surfaces

Cited by in corpus (3)

• Complex Hyperbolic Structures on Disc Bundles over Surfaces
• Quotients of the holomorphic 2-ball and the turnover
• Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamental polyhedra