The symplectic representation of the mapping class group is unique

Abstract

Any nontrivial homomorphism from the mapping class group of an orientable surface of genus $g\ge 3$ to $\GL(2g,\C)$ is conjugate to the standard symplectic representation. It is also shown that the mapping class group has no faithful linear representation in dimensions less than or equal to $3g-3$.

22 pages, 3 figures

References in corpus (4)

• Low-dimensional homology groups of mapping class groups: a survey
• The mapping class group of a genus two surface is linear
• On the linearity of certain mapping class groups
• Triviality of some representations of $MCG(S_g)$ in $GL(n,C),Diff(S^2)$ and $Homeo(T^2)$

Cited by in corpus (3)

• Generalized Long-Moody functors
• Stable twisted cohomology of the mapping class groups in the exterior powers of the unit tangent bundle homology
• On visualization of the linearity problem for mapping class groups of surfaces