A COHOMOLOGICAL LOWER BOUND FOR THE TRANSVERSE LS CATEGORY OF A FOLIATED MANIFOLD

摘要

Let F be a compact Hausdorff foliation on a compact manifold. Let E_2~(>0,·) = ⊕{E_2~(p,q) : p > 0, q ≥ 0} be the subalgebra of cohomology classes with positive transverse degree in the E_2 term of the spectral sequence of the foliation. We prove that the saturated transverse Lusternik-Schnirelmann category of F is bounded below by the length of the cup product in E_2~(>0,·) Other cohomological bounds are discussed.