The mapping class group, MCG, of a closed orientable surface of
genus g has classical symplectic representation coming from its action on
the first
homology of the surface. I will show that any 2g-dimensional nontrivial
representation of the group MCG is conjugate to this classical
representation. I will also prove that MCG has no faithful linear
representation in dimensions less than 3g-2. This contributes to the
well-known problem on the linearity of MCG. Some algebraic corollaries on
representations of related group will be given.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/2846