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July 2017 A finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface
Ryoma Kobayashi, Genki Omori
Osaka J. Math. 54(3): 457-474 (July 2017).

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 $g=3$.

Citation

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Ryoma Kobayashi. Genki Omori. "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 (3) 457 - 474, July 2017.

Information

Published: July 2017
First available in Project Euclid: 7 August 2017

zbMATH: 1375.57024
MathSciNet: MR3685587

Subjects:
Primary: 57M05 , 57M07 , 57M20 , 57M60

Rights: Copyright © 2017 Osaka University and Osaka City University, Departments of Mathematics

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Vol.54 • No. 3 • July 2017
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