G-Actions on Riemann Surfaces and the associated Group of Singular Orbit Data
| dc.creator | Grieder, Ralph | |
| dc.date | 1999-02-06 | |
| dc.date.accessioned | 2026-07-07T05:27:50Z | |
| dc.date.available | 2026-07-07T05:27:50Z | |
| dc.description | Let $G$ be a finite group. To every smooth $G$-action on a compact, connected and oriented Riemann surface we can associate its data of singular orbits. The set of such data becomes an Abelian group $B_G$ under the $G$-equivariant connected sum. The map which sends $G$ to $B_G$ is functorial and carries many features of the representation theory of finite groups. In this paper we will give a complete computation of the group $B_G$ for any finite group $G$. There is a surjection from the $G$-equivariant cobordism group of surface diffeomorphisms $Ω_G$ to $B_G$. We will prove that the kernel of this surjection is isomorphic to $H_2(G;Z)$. Thus $Ω_G$ is an Abelian group extension of $B_G$ by $H_2(G;Z)$. Finally we will prove that the group $B_G$ contains only elements of order two if and only if every complex character of $G$ has values in $R$. This property shows a strong relationship between the functor $B$ and the representation theory of finite groups. | |
| dc.description | 23 pages. See also http://www.math.nwu.edu/~ralph/ | |
| dc.identifier | https://arxiv.org/abs/math/9902048 | |
| dc.identifier | http://arxiv.org/abs/math/9902048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78071 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M60; 57R85; 20C15 (Primary) 58G10 (Secondary) | |
| dc.title | G-Actions on Riemann Surfaces and the associated Group of Singular Orbit Data | |
| dc.type | text |