Geometric and Functional Analysis ( IF 2.4 ) Pub Date : 2024-07-01 , DOI: 10.1007/s00039-024-00682-x Stéphane Guillermou , Claude Viterbo
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.
中文翻译:
滑轮的奇异支撑是 γ 各向同性的
我们证明滑轮派生类别中元素的奇异支撑是 γ 各向同性的,这是 [Vit22] 中定义的概念。我们证明这意味着它在 Kashiwara-Schapira 意义上是对合的,但 γ 各向同性的优点是通过辛同胚不变(而对合性仅通过 C 1 微分同胚不变),并且我们给出一个非 γ 各向同性的对合集的例子。在此过程中,我们证明了许多与奇异支持和谱范数 γ 相关的结果,并提出了许多新问题。