On topological type of periodic self-homeomorphisms of closed non-orientable surfaces
| Autor: | Błażej Szepietowski, Grzegorz Gromadzki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Applied Mathematics 010102 general mathematics Order (ring theory) Cyclic group Type (model theory) Topology 01 natural sciences Mapping class group Combinatorics Computational Mathematics Computer Science::Discrete Mathematics Genus (mathematics) 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Topological conjugacy Orbifold Quotient Analysis Mathematics |
| Zdroj: | Revista DE la Real Academia DE Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas |
| Popis: | Let \(S_g\) denote a closed non-orientable surface of genus \(g\ge 3\). At the beginning of 1980s E. Bujalance showed that the maximum order of a periodic self-homeomorphism of \(S_g\) is equal to 2g or \(2(g-1)\) for g odd or even respectively, and this upper bound is attained for all \(g\ge 3\). In this paper we enumerate, up to topological conjugation, actions on \(S_g\) of a cyclic group \(\mathbb {Z}_N\) of order \(N>g-2\) with prescribed type of the quotient orbifold \(S_g/ {\mathbb {Z}_N}\). We also compute, for a fixed g and N ranging between \(\max \{g,{3(g-2)}/{2}\}\) and 2g, the total numbers of different topological types of action of \(\mathbb {Z}_N\) on \(S_g\). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|