New description of perverse sheaves on a disc

TL;DR

This paper establishes an equivalence between the category of perverse sheaves on a stratified disc and a new category based on 4-periodic semiorthogonal decompositions, linking geometric and categorical concepts.

Contribution

It introduces a novel categorical framework that models perverse sheaves on a stratified disc using 4-periodic semiorthogonal decompositions.

Findings

Proves the equivalence between the new category and perverse sheaves on the stratified disc.

Connects perverse sheaves with spherical functors and semiorthogonal decompositions.

Provides a new categorical perspective on stratified perverse sheaves.

Abstract

There is a connection between the category of perverse sheaves on a disc and different notions related to spherical functors. We introduce a category whose objects are analogous to 4-periodic semiorthogonal decompositions and prove that it is equivalent to the category of perverse sheaves on a disc stratified by the origin and its complement.