Treffer: STABLE QUASICONFORMAL MAPPING CLASS GROUPS AND ASYMPTOTIC TEICHMÜLLER SPACES

Title:
STABLE QUASICONFORMAL MAPPING CLASS GROUPS AND ASYMPTOTIC TEICHMÜLLER SPACES
Authors:
FUJIKAWA, Ege, MATSUZAKI, Katsuhiko
Source:
American journal of mathematics (Print). 133(3):637-675
Publisher Information:
Baltimore, MD: Johns Hopkins University Press, 2011.
Publication Year:
2011
Physical Description:
print, 33 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Géométrie algébrique, Algebraic geometry, Analyse mathématique, Mathematical analysis, Fonctions d'une variable complexe, Functions of a complex variable, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Déformation, Deformation, Deformación, Etat surface, Surface conditions, Estado superficie, Groupe automorphisme, Automorphism group, Grupo automorfismo, Groupe complexe, Complex group, Grupo complejo, Groupe modulaire, Modular group, Grupo modular, Géometrie hyperbolique, Hyperbolic geometry, Geometría hiperbólica, Homéomorphisme, Homeomorphism, Homeomorfismo, Point fixe, Fix point, Punto fijo, Structure groupe, Group structure, Estructura grupo, Surface Riemann, Riemann surface, Superficie Riemann, Variété complexe, Complex manifold, Variedad compleja, Virgule fixe, Fixed point, Coma fija, 14H55, 30Fxx, 32M10, 32Qxx, 37C25, 51M10, 57S05, 58D05, Espace quotient, Groupe classe, Géométrie surface, Mappage quasi conforme, Quasiconformal mapping, Surface hyperbolique
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
DEPARTMENT OF MATHEMATICS, CHIBA UNIVERSITY, 1-33 YAYOI-CHO, INAGE-KU, CHIBA 263-8522, Japan
DEPARTMENT OF MATHEMATICS, SCHOOL OF EDUCATION, WASEDA UNIVERSITY, SHINJUKU, TOKYO 169-8050, Japan
ISSN:
0002-9327
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=24196662
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24196662
Database:
PASCAL Archive

Weitere Informationen

The stable quasiconformal mapping class group is a group of quasiconformal mapping classes of a Riemann surface that are homotopic to the identity outside some topologically finite subsurface. Its analytic counterpart is a group of mapping classes that act on the asymptotic Teichmüller space trivially. We prove that the stable quasiconformal mapping class group is coincident with the asymptotically trivial mapping class group for every Riemann surface satisfying a certain geometric condition. Consequently, the intermediate Teichmüller space, which is the quotient space of the Teichmüller space by the asymptotically trivial mapping class group, has a complex manifold structure, and its automorphism group is geometrically isomorphic to the asymptotic Teichmüller modular group. The proof utilizes a condition for an asymptotic Teichmüller modular transformation to be of finite order, and this is given by the consideration of hyperbolic geometry of topologically infinite surfaces and its deformation under quasiconformal homeomorphisms. Also these arguments enable us to show that every asymptotic Teichmüller modular transformation of finite order has a fixed point on the asymptotic Teichmüller space, which can be regarded as an asymptotic version of the Nielsen theorem.