Automorphisms of curve complexes on nonorientable surfaces

Download

index.pdf

Date

2014-01-01

Author

Atalan, Ferihe
Korkmaz, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

341
views

134
downloads

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.

Subject Keywords

Mapping class group, Complex of curves, Nonorientable surface

URI

https://hdl.handle.net/11511/34915

Journal

GROUPS GEOMETRY AND DYNAMICS

DOI

https://doi.org/10.4171/ggd/216

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Torsion Generators Of The Twist Subgroup Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01) We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.
Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or by Three Involutions Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-01-01) We prove that, for g≥ 19 the mapping class group of a nonorientable surface of genus g, Mod (Ng) , can be generated by two elements, one of which is of order g. We also prove that for g≥ 26 , Mod (Ng) can be generated by three involutions.
Mapping class groups of nonorientable surfaces Korkmaz, Mustafa (2002-02-01) We obtain a finite set of generators for the mapping class group of a nonorientable surface with punctures. We then compute the first homology group of the mapping class group and certain subgroups of it. As an application we prove that the image of a homomorphism from the mapping class group of a nonorientable surface of genus at least nine to the group of real-analytic diffeomorphisms of the circle is either trivial or of order two.
Equivariant Picard groups of the moduli spaces of some finite Abelian covers of the Riemann sphere Ozan, Yıldıray (2023-03-01) In this note, following Kordek's work we will compute the equivariant Picard groups of the moduli spaces of Riemann surfaces with certain finite abelian symmetries.
A note on the generalized Matsumoto relation DALYAN, ELİF; Medetogullari, Elif; Pamuk, Mehmetcik (2017-01-01) We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.

Citation Formats

F. Atalan and M. Korkmaz, “Automorphisms of curve complexes on nonorientable surfaces,” GROUPS GEOMETRY AND DYNAMICS, pp. 39–68, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34915.