Mapping class group is generated by three involutions

Date

2020-01-01

Author

Korkmaz, Mustafa

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We prove that the mapping class group of a closed connected orientable surface of genus at least eight is generated by three involutions.

URI

https://hdl.handle.net/11511/70236

Journal

MATHEMATICAL RESEARCH LETTERS

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Department of Mathematics, Article

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The mapping class group is generated by two commutators Baykur, R. Inanc; Korkmaz, Mustafa (2021-05-01) We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators. (C) 2021 Elsevier Inc. All rights reserved.
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.
Automorphisms of curve complexes on nonorientable surfaces Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01) 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.
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.
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.

Citation Formats

M. Korkmaz, “Mapping class group is generated by three involutions,” MATHEMATICAL RESEARCH LETTERS, pp. 1095–1108, 2020, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/70236.