For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g+n≥5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
Classification :
57-XX, 20-XX
Mots-clés :
Mapping class group, complex of curves, nonorientable surface
Affiliations des auteurs :
Ferihe Atalan
1
;
Mustafa Korkmaz
2
1
Atilim University, Ankara, Turkey
2
Middle East Technical University, Ankara, Turkey
Ferihe Atalan; Mustafa Korkmaz. Automorphisms of curve complexes on nonorientable surfaces. Groups, geometry, and dynamics, Tome 8 (2014) no. 1, pp. 39-68. doi: 10.4171/ggd/216
@article{10_4171_ggd_216,
author = {Ferihe Atalan and Mustafa Korkmaz},
title = {Automorphisms of curve complexes on nonorientable surfaces},
journal = {Groups, geometry, and dynamics},
pages = {39--68},
year = {2014},
volume = {8},
number = {1},
doi = {10.4171/ggd/216},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/216/}
}
TY - JOUR
AU - Ferihe Atalan
AU - Mustafa Korkmaz
TI - Automorphisms of curve complexes on nonorientable surfaces
JO - Groups, geometry, and dynamics
PY - 2014
SP - 39
EP - 68
VL - 8
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/216/
DO - 10.4171/ggd/216
ID - 10_4171_ggd_216
ER -
%0 Journal Article
%A Ferihe Atalan
%A Mustafa Korkmaz
%T Automorphisms of curve complexes on nonorientable surfaces
%J Groups, geometry, and dynamics
%D 2014
%P 39-68
%V 8
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/216/
%R 10.4171/ggd/216
%F 10_4171_ggd_216
