Perverse Schobers

By M. Kapranov, V. Schechtman. 2014

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We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples, giving a natural but ad hoc definition in each case. In the simplest case (perverse sheaves on a disk with one possible singular point) we propose, as a categorical analog, the data of a spherical functor.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed1662e1e387004fdbff73edf762fdea1e01ebd3