Sheaf quantization of Legendrian isotopy. Issue 2 (17th February 2023)

• Record Type: Journal Article
• Authors: Zhou, Peng
• Is Part Of: Compositio mathematica. Volume 159:Issue 2(2023)
• Page Start: 419
• Page End: 435
• Publication Date: 2023-02-17
• Subjects: nearby cycle -- singular support estimate; 53D25 -- 53D37; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X2200793X
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : Let $\{\Lambda ^\infty _t\}$ be an isotopy of Legendrians (possibly singular) in a unit cosphere bundle $S^*M$ that arise as slices of a singular Legendrian $\Lambda _I^\infty \subset S^*M \times T^*I$ . Let $\mathcal {C}_t = Sh(M, \Lambda ^\infty _t)$ be the differential graded derived category of constructible sheaves on $M$ with singular support at infinity contained in $\Lambda ^\infty _t$ . We prove that if the isotopy of Legendrians embeds into an isotopy of Liouville hypersurfaces, then the family of categories $\{\mathcal {C}_t\}$ is constant in $t$ .