I am looking for a suitable set of Dehn-twists generators for the mapping class group of a curve of genus $g$ with $n$ marked points (i.e. the mapping class group of $\mathcal M_{g,n}$).

For $\mathcal M_g$ one can use $2g+1$ Dehn twists, and also choose them as non-separating loops (i.e. they do not split the surface in two disconnected components). This is what I need.

For $\mathcal M_{g,n}$ I would imagine that one should add $n-1$ ($n$?) extra Dehn twists around pairs of marked points to generate the elementary braids. Since I am not well read in the topic I am looking for information/references.

Ideally I would like that there exist a suitable number ($2g+n$ more or less) of Dehn twists, each of which have the following generalized nonseparating property;

either they do not separate the pointed curve or they separate but in each component there is at least one puncture.

Thanks for your help!


The answer to your question can be found on page 114 of Farb-Margalit's Primer on Mapping Class Groups. See Figure 4.10. All the Dehn twists they list are actually nonseparating curves.


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