Brane structures in microlocal sheaf theory

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2024-03-14 DOI:10.1112/topo.12325

Xin Jin, David Treumann

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引用次数: 0

Abstract

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

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微局域剪切理论中的线性结构

让 L$L$ 成为共切束 T∗M$T^* M$ 的精确拉格朗日子平面，渐近于 Legendrian 子平面Λ⊂T∞M$\Lambda \subset T^{\infty } M$ 。M$.我们研究的是 L$L$ 上的∞$\infty$-类的局部常数层，称为 "蝶恋花结构层 "或 "BraneL$\mathrm{Brane}_L$"。它的纤维是光谱的∞$infty$类别，我们构建了一个从Γ(L,BraneL)$\Gamma (L,\mathrm{Brane}_L)$到 M$M$ 上具有Λ$Lambda$奇异支持的光谱剪切的∞$infty$类别的哈密顿不变全忠函数。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.