The symplectic representation of the mapping class group is unique

2011/08/16 by Korkmaz, Mustafa
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1108.3241

Abstract

Any nontrivial homomorphism from the mapping class group of an orientable surface of genus g≥ 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.

Related

• Low-dimensional linear representations of mapping class groups
• Linear representations of the mapping class group of dimension at most 3g-3
• A note on minimal finite quotients of mapping class groups
• Mapping class groups are not linear in positive characteristic
• On the surjectivity of the Symplectic representation of the mapping class group