Poincaré duality angles and the Dirichlet-to-Neumann operator

Abstract

On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. This paper solves the inverse problem of recovering the relative positions of these subspaces from the Cauchy data for differential forms. This solution is also exploited to partially resolve a question of Belishev and Sharafutdinov about whether the Cauchy data for differential forms determine the cup product structure on a manifold with boundary.