A finiteness theorem for the spectral sequence of a Riemannian foliation
Jesús A. Álvarez López · Illinois Journal of Mathematics · 1989
basic cohomology, [which is equal to E'(')) is finite-dimensional. They prove it step to step for Lie foliations, transversely parallelizable foliations andRiemannian foliations.This paper establishes the following improvement of the two results above. THEOREM. If a smooth closed manifold M carries a Riemannian foliation then E 2 (') is finite-dimensionaLTo prove it we assume that '^is transvers^ely oriented and construct an operation of a Lie algebra in E('), where " is the horizontal lift of " to the principal fiberbundle of oriented orthonormal frames with the transverse