Tohoku Mathematical Journal
2024
June
SECOND SERIES VOL. 76, NO. 2

Tohoku Math. J.
76 (2024), 229-253

Title AN INFINITE PRESENTATION FOR THE TWIST SUBGROUP OF THE MAPPING CLASS GROUP OF A COMPACT NON-ORIENTABLE SURFACE

Author Ryoma Kobayashi and Genki Omori

(Received June 2, 2022, revised November 21, 2022)
Abstract. A finite presentation for the subgroup of the mapping class group of a compact non-orientable surface generated by all Dehn twists was given by Stukow [26]. In this paper, we give an infinite presentation for this group, mainly using the presentation given by Stukow [26] and Birman exact sequences on mapping class groups of non-orientable surfaces.

Mathematics Subject Classification. Primary 20F05; Secondary 57M07.
Key words and phrases. Mapping class group, twist subgroup, presentation.

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