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2018/6/25(Mon)

15:00--16:00 E404


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The right-angled Artin groups on the complement graphs of path graphs in mapping class groups

This is a joint work with Takuya Katayama. Let $\Gamma$ be a finite graph without loops or multi-edges. In 2015, Kim-Koberda proved that for any $\Gamma$ there exists a positive integer $p$ such that the right-angled Artin group $A(\Gamma)$ on $\Gamma$ is a subgroup of the pure braid group $PB_{p}$ on $p$-strands. Our main concern is to decide whether $A(\Gamma)$ is a subgroup of $PB_{p}$, the braid group $B_{p}$ on $p$-strands, and more generally, the mapping class group of an orientable surface for given $\Gamma$. In this talk, we solve this problem for the complement graphs of path graphs.