Brane structures in microlocal sheaf theory

Abstract

Let (Formula presented.) be an exact Lagrangian submanifold of a cotangent bundle (Formula presented.), asymptotic to a Legendrian submanifold (Formula presented.). We study a locally constant sheaf of (Formula presented.) -categories on (Formula presented.), called the sheaf of brane structures or (Formula presented.). Its fiber is the (Formula presented.) -category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from (Formula presented.) to the (Formula presented.) -category of sheaves of spectra on (Formula presented.) with singular support in (Formula presented.).