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- W4306295040 abstract "For a subanalytic Legendrian $Lambda subset S^{*}M$, we prove that when $Lambda$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_Lambda: operatorname{Sh}_Lambda(M) rightarrow operatorname{mu sh}_Lambda(Lambda)$ is a spherical functor, and the spherical cotwist is the Serre functor on the subcategory $operatorname{Sh}_Lambda^b(M)_0$ of compactly supported sheaves with perfect stalks. In this case, when $M$ is compact the Verdier duality on $operatorname{Sh}_Lambda^b(M)$ extends naturally to all compact objects $operatorname{Sh}_Lambda^c(M)$. This is a sheaf theory counterpart (with weaker assumptions) of the results on the cap functor and cup functors between Fukaya categories. When proving spherical adjunction, we deduce the Sato-Saboff fiber sequence and construct the Guillermou doubling functor for any Reeb flow. As a setup for the Verdier duality statement, we study the dualizability of $operatorname{Sh}_Lambda(M)$ itself and obtain a classification result of colimit-preserving functors by convolutions of sheaf kernels." @default.
- W4306295040 created "2022-10-15" @default.
- W4306295040 creator A5027341812 @default.
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- W4306295040 date "2022-10-12" @default.
- W4306295040 modified "2023-09-27" @default.
- W4306295040 title "Duality and spherical adjunction from microlocalization -- An approach by contact isotopies" @default.
- W4306295040 doi "https://doi.org/10.48550/arxiv.2210.06643" @default.
- W4306295040 hasPublicationYear "2022" @default.
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