## Brane structures from the perspective of microlocal sheaf theory

symplectic topology. For every closed exact Lagrangian L in the cotangent bundle of a manifold

M, we associate a locally constant sheaf of categories on L, which we call Brane_L, whose fiber is

the infinity-category of k-modules, for k any ring spectrum. I will discuss the relation of Brane_L

with the usual brane structures in Floer theory, and its connection to the J-homomorphism in