Groups, Geometry, and Dynamics

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Volume 8, Issue 1, 2014, pp. 39–68
DOI: 10.4171/GGD/216

Published online: 2014-05-13

Automorphisms of curve complexes on nonorientable surfaces

Ferihe Atalan[1] and Mustafa Korkmaz[2]

(1) Atilim University, Ankara, Turkey
(2) Middle East Technical University, Ankara, Turkey

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 $g+n \geq 5$. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.

Keywords: Mapping class group, complex of curves, nonorientable surface

Atalan Ferihe, Korkmaz Mustafa: Automorphisms of curve complexes on nonorientable surfaces. Groups Geom. Dyn. 8 (2014), 39-68. doi: 10.4171/GGD/216