Categories associated to punctured surfaces and surface braid twist group actions on triangulated categories
Sebastian Opper
Charles University, Prague, Czech Republic
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Abstract
We give an overview on group actions on triangulated categories induced by collections of spherical objects, guided by the question of which structure such groups attain. In this context we discuss an ongoing joint project of the author with Wassilij Gnedin and Alexandra Zvonareva on graded generalisations of Brauer graph algebras associated to suitably decorated punctured surfaces and conjectural faithful actions by surface braid twist groups via spherical twists.