Name Byung Hee An POSTECH Session Jan 9 15:20~15:50 E11-102 Geometric automorphisms of braid groups on surfaces Let $\Sigma$ be a compact, connected, orientable surface of genus $g\ge 1$ with boundary and $\bar{\mathbf{x}}^0=\{x_1^0,\dots,x_n^0\}$ be a distinct points in the interior of $\Sigma$. Then the braid group $\mathbf{B}_n(\Sigma,\bar{\mathbf{x}}^0)$ is defined as the fundamental group of configuration space. For given automorphism $\phi$ on $\mathbf{B}_n(\Sigma,\bar{\mathbf{x}}^0)$, we say that $\phi$ is {\em geometric} if there exists an automorphism $f$ on $(\Sigma,\bar{\mathbf{x}}^0)$ such that the induced map $f_*$ on $\mathbf{B}_n(\Sigma,\bar{\mathbf{x}}^0)$ is $\phi$. In this talk, we present the necessary and sufficient condition for $\phi$ to be geometric. 102-1-9/Geometric_automorphims_of_braid_groups_on_surfaces.pdf