Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary
Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary
In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an extension theorem for basic forms of induced Riemannian foliation on the boundary. We prove the complex …