A presentation for the mapping class group of a nonorientable surface

Paris, Luis; Szepietowski, Błażej

doi:10.24033/bsmf.2697

A presentation for the mapping class group of a nonorientable surface
[Une présentation du mapping class groupe d'une surface non orientable]

Paris, Luis ; Szepietowski, Błażej

Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 503-566

Abstract (VO)
Résumé

Let $N_{g, n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $ℳ (N_{g, n})$ its mapping class group. We obtain an explicit finite presentation of $ℳ (N_{g, n})$ for $n \in {0, 1}$ and all $g$ such that $g + n > 3$ .

Notons $N_{g, n}$ la surface non orientable de genre $g$ avec $n$ composantes de bord et $ℳ (N_{g, n})$ son mapping class groupe. On obtient une présentation finie explicite de $ℳ (N_{g, n})$ pour $n \in {0, 1}$ et pour tout $g$ tel que $g + n > 3$ .

Publié le : 2015-07-21

MR

DOI : 10.24033/bsmf.2697

Classification : 57M07, 20F38, 57N05
Keywords: Mapping class group, nonorientable surface, group presentation.
Mots-clés : Mapping class groupe, surface non-orientable, présentation de groupe.

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     author = {Paris, Luis and Szepietowski, B{\l}a\.zej},
     title = {A presentation for the mapping class group of a nonorientable surface},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {503--566},
     year = {2015},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {3},
     doi = {10.24033/bsmf.2697},
     mrnumber = {3417732},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2697/}
}

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Paris, Luis; Szepietowski, Błażej. A presentation for the mapping class group of a nonorientable surface. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 503-566. doi: 10.24033/bsmf.2697

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