Wrapped microlocal sheaves on pairs of pants
David Nadler

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons
