THE PILLAR SWITCHINGS OF MAPPING CLASS GROUPS OF SURFACES
THE PILLAR SWITCHINGS OF MAPPING CLASS GROUPS OF SURFACES
The braid group $B_g$ is embedded in the ribbon braid group that is defined to be the mapping class group $Γ_{0,(g),1}$. By gluing two copies of surface $S_{0,g+2}$ along $g+1$ holes, we get surface $S_{g,1}$. A pillar switching is a self-homeomorphism of $S_{g,1}$ which switches two pillars of surfaces by …