Involutions of compact Klein surfaces
type: Item
instance of: scholarly article
title: Involutions of compact Klein surfaces
zbMATH Open document ID: 0758.30036
DOI: 10.1007/BF02571439
author: Antonio F. Costas
author: Emilio Bujalance
author: Sergey Natanzon
author: David Singerman
published in: Mathematische Zeitschrift
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174452
review text: Let \(X\) be a compact Klein surface and let \(\varphi: X\to X\) be a dianalytic involution. We determine \(\varphi\) up to topological conjugacy by a finite number of invariants mainly connected with the fixed point set of \(\varphi\). These results generalize classical results of F. Klein for Riemann surfaces without boundary and of W. Scherrer for non-orientable surfaces without boundary. We investigate corresponding inclusions between non- Euclidean crystallographic groups and use these to consider the spaces of Teichmüller and moduli spaces of Klein surfaces admitting involutions.
Mathematics Subject Classification ID: 30F50
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 126407
zbMATH Keywords: dianalytic involution
zbMATH Keywords: fixed point set
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: non-Euclidean crystallographic groups
zbMATH Keywords: Klein surfaces
reviewed by: Emilio Bujalance
MaRDI profile type: Publication
cites work: Normal N.E.C. signatures
cites work: Normal subgroups of even index in an NEC group
cites work: On Branch Loci in Teichmuller Space
cites work: Q3950733
cites work: The Classification of Non-Euclidean Plane Crystallographic Groups
cites work: SMOOTH COVERINGS OF HYPERELLIPTIC SURFACES
cites work: Klein surfaces
cites work: Topological classification of pairs of commuting antiholomorphic involutions of Riemann surfaces
cites work: Q4771443
cites work: On non-Euclidean crystallographic groups
OpenAlex ID: W1981424288
description: scientific article; zbMATH DE number 126407