Hiroshima Mathematical Journal

A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists

Genki Omori

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Abstract

We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hirose [5].

Article information

Source
Hiroshima Math. J., Volume 48, Number 1 (2018), 81-88.

Dates
Received: 10 April 2017
Revised: 9 August 2017
First available in Project Euclid: 8 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1520478025

Digital Object Identifier
doi:10.32917/hmj/1520478025

Mathematical Reviews number (MathSciNet)
MR3772002

Zentralblatt MATH identifier
06901789

Subjects
Primary: 20F05: Generators, relations, and presentations 57M07: Topological methods in group theory 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms

Keywords
mapping class group non-orientable surface Dehn twist

Citation

Omori, Genki. A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. Hiroshima Math. J. 48 (2018), no. 1, 81--88. doi:10.32917/hmj/1520478025. https://projecteuclid.org/euclid.hmj/1520478025


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