Osaka Journal of Mathematics

A finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface

Ryoma Kobayashi and Genki Omori

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Abstract

We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove that the level 2 twist subgroup is normally generated in the mapping class group by a crosscap pushing map along a non-separating two-sided simple loop for genus $g\geq 5$ and $g=3$. As an application, we calculate the first homology group of the level 2 twist subgroup for genus $g\geq 5$ and $g=3$.

Article information

Source
Osaka J. Math., Volume 54, Number 3 (2017), 457-474.

Dates
First available in Project Euclid: 7 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1502092823

Mathematical Reviews number (MathSciNet)
MR3685587

Zentralblatt MATH identifier
1375.57024

Subjects
Primary: 57M05: Fundamental group, presentations, free differential calculus 57M07: Topological methods in group theory 57M20: Two-dimensional complexes 57M60: Group actions in low dimensions

Citation

Kobayashi, Ryoma; Omori, Genki. A finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. Osaka J. Math. 54 (2017), no. 3, 457--474. https://projecteuclid.org/euclid.ojm/1502092823


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