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arXiv · 1704.04291

Brane structures in microlocal sheaf theory

Xin Jin·David Treumann
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Abstract

Let $L$ be an exact Lagrangian submanifold of a cotangent bundle $T^* M$, 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 $\Lambda$.

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Xin Jin, David Treumann. 2017-04-13. Brane structures in microlocal sheaf theory. https://doi.org/10.1112/topo.12325

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