Brane structures in microlocal sheaf theory

Abstract

Let $L$ be an exact Lagrangian submanifold of a cotangent bundle $T^{\ast }M$, asymptotic to a Legendrian submanifold $\Lambda \subset T^{\infty }M$. We study a locally constant sheaf of $\infty$-categories on $L$, called the sheaf of brane structures or ${\mathrm{Brane}}_L$. Its fiber is the $\infty$-category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from $\Gamma (L,{\mathrm{Brane}}_L)$ to the $\infty$-category of sheaves of spectra on $M$ with singular support in $\Lambda$.

59 pages, 18 figures

References in corpus (1)

• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology

Cited by in corpus (3)

• Compact sheaves on a locally compact space
• Lagrangian cobordism and shadow distance in Tamarkin category
• Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop