Revisiting Poincar\'e's Theorem on presentations of discontinuous groups via fundamental polyhedra
| Autor: | Eric Jespers, Á. del Río, Ann Kiefer |
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| Přispěvatelé: | Algebra |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Presentations Riemann manifold 20H10 30F40 Covering space General Mathematics Fundamental Domains Mathematical proof Constructive Kleinian groups Constant curvature symbols.namesake Polyhedron Fundamental domain Poincaré conjecture symbols Mathematics - Group Theory Discontinuous groups Mathematics |
| Popis: | We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only makes use of basic geometric concepts. In a sense one hence obtains a proof that is of a more constructive nature than most known proofs. Comment: 38 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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