An obstruction to embedding right-angled Artin groups in mapping class groups

Sang-hyun Kim; Thomas Koberda

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arXiv · 1207.5498

An obstruction to embedding right-angled Artin groups in mapping class groups

Sang-hyun Kim·Thomas Koberda

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Abstract

For every orientable surface of finite negative Euler characteristic, we find a right-angled Artin group of cohomological dimension two which does not embed into the associated mapping class group. For a right-angled Artin group on a graph $\gam$ to embed into the mapping class group of a surface $S$, we show that the chromatic number of $\gam$ cannot exceed the chromatic number of the clique graph of the curve graph $\mathcal{C}(S)$. Thus, the chromatic number of $\gam$ is a global obstruction to embedding the right-angled Artin group $A(\gam)$ into the mapping class group $\Mod(S)$.

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BibTeX RIS

Sang-hyun Kim, Thomas Koberda. 2012-10-09. An obstruction to embedding right-angled Artin groups in mapping class groups. https://arxiv.org/abs/1207.5498

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