Groups, Geometry, and Dynamics
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Published online: 2014-05-13
Automorphisms of curve complexes on nonorientable surfacesFerihe Atalan and Mustafa Korkmaz (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