剪切的奇异支持是 γ-各向异性的

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-07-01 DOI:10.1007/s00039-024-00682-x

Stéphane Guillermou, Claude Viterbo

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引用次数: 0

摘要

我们证明了剪子的派生范畴中元素的奇点支持是 γ-各向异性的，这是[Vit22]中定义的一个概念。我们证明这意味着它是柏原-沙皮拉意义上的各向异性，但是γ-各向异性的优势在于它是交映同构不变的（而各向异性只在 C1 差分同构中不变），并且我们给出了一个不具有γ-各向异性的各向异性集合的例子。在此过程中，我们证明了一系列与奇异支持和谱规范 γ 有关的结果，并提出了一些新问题。

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The Singular Support of Sheaves Is γ-Coisotropic

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The Singular Support of Sheaves Is γ-Coisotropic

We prove that the singular support of an element in the derived category of sheaves is γ-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being γ-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by C¹ diffeomorphisms) and we give an example of an involutive set that is not γ-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm γ and raise a number of new questions.

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.