Sheaf Quantization of Legendrian Isotopy

Abstract

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

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