Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
131
views
0
downloads
Cite This
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
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.
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.
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
Generating the twist subgroup by involutions
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2020-01-01)
For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group generated by Dehn twists about two-sided simple closed curves. In this paper, we consider involution generators of the twist subgroup and give generating sets of involutions with smaller number of generators than the ones known in the literature using new techniques for finding involution generators.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.