Osaka Journal of Mathematics

The twist subgroup of the mapping class group of a nonorientable surface

Michał Stukow

Full-text: Open access

Abstract

Let $\mathcal{T}(N)$ be the subgroup of the mapping class group of a nonorientable surface $N$ (possibly with punctures and/or boundary components) generated by twists about two-sided circles. We obtain a simple generating set for $\mathcal{T}(N)$. As an application we compute the first homology group (abelianization) of $\mathcal{T}(N)$.

Article information

Source
Osaka J. Math., Volume 46, Number 3 (2009), 717-738.

Dates
First available in Project Euclid: 26 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1256564203

Mathematical Reviews number (MathSciNet)
MR2583326

Zentralblatt MATH identifier
1193.57009

Subjects
Primary: 57N05: Topology of $E^2$ , 2-manifolds
Secondary: 20F38: Other groups related to topology or analysis 57M99: None of the above, but in this section

Citation

Stukow, Michał. The twist subgroup of the mapping class group of a nonorientable surface. Osaka J. Math. 46 (2009), no. 3, 717--738. https://projecteuclid.org/euclid.ojm/1256564203


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