代数幾何学セミナー


2017/11/24(Fri)

16:30--18:00 E404/406/408

JongMyeong Kim

Nagoya univ.

A freeness criterion for spherical twists

Spherical twists along spherical objects are autoequivalences of a triangulated category defined by Seidel and Thomas as a categorical analog of Dehn twists along simple closed curves. Spherical twists share many properties with Dehn twists. On the other hand, there is a classical result by Humphries which states that if a collection of simple closed curves admits a "complete partition" and does not bound a disk then the group generated by the Dehn twists along them is isomorphic to the free product of free abelian groups. In this talk, we give a categorical analog of Humphries' argument.