Name  Byung Hee An 

Affiliation  POSTECH 
Talk type  Session 
Time  Jan 9 15:20~15:50 
Location  E11102 
Title  Geometric automorphisms of braid groups on surfaces 
Abstract 
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.

Slide  10219/Geometric_automorphims_of_braid_groups_on_surfaces.pdf 