Oscar Harr: Stokes theorem and characteristic classes of manifold bundles

Abstract

The family Stokes theorem is an equation relating fiber integration along a bundle of manifolds (with boundary) and its associated boundary bundle. We lift this equation to a commutative diagram in the derived category of sheaves on the base space of the family, with coefficients in an arbitrary presentably symmetric monoidal stable \(\infty\)-category. Using this diagram, we deduce new relations among characteristic classes of bundles of manifolds with boundary.