Abstract: |
Perverse schobers are a (in general still conjectural) categorification of the notion of perverse sheaves, where vector spaces are replaced by enhanced triangulated categories. The notion was proposed by Kapranov-Schechtman in 2014. We will begin with a gentle introduction and overview over perverse sheaves and perverse schobers. After that, the focus will be on perverse schobers on the cotangent bundles of surfaces. The codimension 1 stratum will be given by a surface as well, called the spectral curve, which forms a simple branched covering of the base. To define/describe perverse schobers, we will categorify a description of perverse sheaves in this setting due to Gelfand-MacPherson-Vilonen (Duke '96). |