叶状流形的横截LS范畴的上同调下界
A cohomological lower bound for the transverse LS category of a foliated manifold
摘要：
设$\mathcal{F}$是紧致流形上的紧致Hausdorff叶状。设${E_2^{>0,\bullet}}=\oplus\{E_2^{p,q}\colon p>0,q\geq 0\}$是叶理的谱序列的$E_2$项中横截度为正的上同调类的子代数.证明了$\mathcal{F}$的饱和横截Lusternik-Schnirelmann范畴在${E_2^{>0,\bullet}}$中的上积的长度下有界.其他上同调的界限进行了讨论。
英文摘要：
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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