1 results
Sheaf quantization of Legendrian isotopy
- Part of
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- Journal:
- Compositio Mathematica / Volume 159 / Issue 2 / February 2023
- Published online by Cambridge University Press:
- 17 February 2023, pp. 419-435
- Print publication:
- February 2023
-
- Article
- Export citation
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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 
$t$.
