2014/07/31 by Yu Qiu · 1 citation
Mathematics · #math.RT #math.AG #math.CT #math.GT
paper · pdf · doi:10.1007/s00208-015-1339-0
published as Math. Ann. 365(2016), pp 595-633 · Updated version
arxiv created 2018/02/24 · arxiv updated 2018/02/27
We are interested in the 3-Calabi-Yau categories D arising from quivers with potential associated to a triangulated marked surface S (without punctures). We prove that the spherical twist group ST of D is isomorphic to a subgroup (generated by braid twists) of the mapping class group of the decorated marked surface S\bigtriangleup. Here S\bigtriangleup is the surface obtained from S by decorating with a set of decorated points, where the number of points equals the number of triangles in any triangulations of S. For instance, when S is an annulus, the result implies the corresponding spaces of stability conditions on D is contractible.