Microlocal Sheaves on Pinwheels

TL;DR

This paper investigates the wrapped Fukaya category and microlocal sheaves on the pinwheel skeleton of a rational homology ball, providing explicit calculations for a specific case and demonstrating their equivalence.

Contribution

It offers explicit calculations of wrapped Fukaya categories and microlocal sheaves on pinwheels, showing their equivalence in a particular case.

Findings

Wrapped Fukaya category and microlocal sheaves match for q=1.

Explicit calculations for the case q=1.

Establishes equivalence between two categories in this setting.

Abstract

In this thesis, we study the wrapped Fukaya category of the rational homology ball $B_{p,q}$ and the traditional/wrapped microlocal sheaves on its skeleton $L_{p,q}$, called pinwheel. We explicitly calculate both for $q=1$, and show they match in wrapped case.