A cohomological lower bound for the transverse LS category of a foliated manifold

Details A cohomological lower bound for the transverse LS category of a foliated manifold A cohomological lower bound for the transverse LS category of a foliated manifold

2008-12-25

arxiv.org/abs/0812.4626v1

Mathematics

Algebraic Topology

9 pages

Scientific paper

Let $\mathcal{F}$ be a compact Hausdorff foliation on a compact manifold. Let ${E_2^{>0,\bullet}}=\oplus\{E_2^{p,q}\colon p>0,q\geq 0\}$ 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 $\mathcal{F}$ is bounded below by the length of the cup product in ${E_2^{>0,\bullet}}$. Other cohomological bounds are discussed.

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