Year: 2011
Type: preprint
Abstract: Recently, John Franks and Michael Handel proved that, for $g\geq 3$ and $n\leq 2g-4$, every homomorphism from the mapping class group of an orientable surface of genus $g$ to $\GL (n,\C)$ is trivial. We extend this result to $n\leq 2g-1$, also covering the case $g=2$. As an application, we prove the corresponding result for nonorientable surfaces. Another application is on the triviality of homomorphisms from the mapping class group of a closed surface of genus $g$ to $\Aut (F_n)$ or to $\Out (F_n)$ for $n\leq 2g-1$.
Source: arXiv (Cornell University)
Author: Korkmaz, Mustafa
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4384408252