Wrapped microlocal sheaves on pairs of pants

TL;DR

This paper introduces wrapped microlocal sheaves inspired by wrapped Fukaya categories, establishing their relation to traditional microlocal sheaves and computing examples on pairs of pants to support mirror symmetry conjectures.

Contribution

It defines wrapped microlocal sheaves, proves their equivalence to traditional microlocal sheaves, and computes them explicitly on higher-dimensional pairs of pants.

Findings

Wrapped microlocal sheaves are equivalent to functionals on traditional microlocal sheaves.

Explicit calculations of wrapped microlocal sheaves on pairs of pants.

Supports mirror symmetry predictions through these computations.

Abstract

Inspired by the geometry of wrapped Fukaya categories, we introduce the notion of wrapped microlocal sheaves. We show that traditional microlocal sheaves are equivalent to functionals on wrapped microlocal sheaves, in analogy with the expected relation of infinitesimal to wrapped Fukaya categories. As an application, we calculate wrapped microlocal sheaves on higher-dimensional pairs of pants, confirming expectations from mirror symmetry.