Sheaf Quantization of Legendrian Isotopy

Abstract

Let $\{Λ^\infty_t\}$ be an isotopy of Legendrians (possibly singular) in a unit cosphere bundle $S^*M$. Let $Sh(M, Λ^\infty_t)$ be the differential graded (dg) derived category of constructible sheaves on $M$ with singular support at infinity contained in $Λ^\infty_t$. We prove that if the isotopy of Legendrians embeds into an isotopy of Weinstein hypersurfaces, then the categories $Sh(M, Λ^\infty_t)$ are invariant.

v1:19 pages, 3 figures. v2: updated Prop 2.12's condition