The symplectic representation of the mapping class group is unique

Details The symplectic representation of the mapping class group is unique The symplectic representation of the mapping class group is unique

2011-08-16

arxiv.org/abs/1108.3241v1

Mathematics

Geometric Topology

22 pages, 3 figures

Scientific paper

Any nontrivial homomorphism from the mapping class group of an orientable
surface of genus $g\geq 3$ 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 $3g-3$.

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