TITLE: Do the following set of Dehn twists generate the mapping class group?
QUESTION [7 upvotes]: If $S$ is the surface illustrated below, do the Dehn twists about the red curves generate the mapping class group $\operatorname{MCG}(S,\partial S)$?

http://math.stanford.edu/~pardon/img/dehntwists.png

REPLY [10 votes]: Humphries arguments are in 
Humphries, Stephen P.
Generators for the mapping class group. Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977), pp. 44–47,
Lecture Notes in Math., 722, Springer, Berlin, 1979. 
The key argument for the $\ne 2g$ case is that the symplectic group $Sp(2g, \mathbf F_2)$  is not generated by $2g$ transvections (which maybe was well known). Steve and I joined up to present this argument and more in our paper 
``Orbits under symplectic
transvections II:  the case  $K=\bf F_2$'', Proc. London
Math. Soc. (3) 52 (1986) 532-556.
and Steve followed this up with much more work in this area.