## Osaka Journal of Mathematics

### A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves

Błażej Szepietowski

#### Abstract

We study the action of the mapping class group $\mathcal{M}(F)$ on the complex of curves of a non-orientable surface $F$. Following the outline of [1] we obtain, using the result of [4], a presentation for $\mathcal{M}(F)$ defined in terms of the mapping class groups of the complementary surfaces of collections of curves, provided that $F$ is not sporadic, i.e. the complex of curves of $F$ is simply connected. We also compute a finite presentation for the mapping class group of each sporadic surface.

#### Article information

Source
Osaka J. Math., Volume 45, Number 2 (2008), 283-326.

Dates
First available in Project Euclid: 15 July 2008

https://projecteuclid.org/euclid.ojm/1216151101

Mathematical Reviews number (MathSciNet)
MR2441942

Zentralblatt MATH identifier
1152.57019

#### Citation

Szepietowski, Błażej. A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves. Osaka J. Math. 45 (2008), no. 2, 283--326. https://projecteuclid.org/euclid.ojm/1216151101

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