空间的（余）链型水平的上、下界
Upper and lower bounds of the (co)chain type level of a space
摘要：
我们建立了拉回纤维化的全空间的上链型能级的一个上界。它解释了为什么球面上的主丛的数值不变量小于或等于2。此外，还给出了道路空间和Borel构造，包括双商空间和Davis-Januszkiewicz空间的水平的计算实例.我们还证明了映射的同伦纤维的链型水平大于Kahl意义下的E-范畴，这是映射的Lusternik-Schnirelmann范畴的代数近似.这个不等式适用于同伦纤维的上同调的阶数和投射维数之间。
英文摘要：
We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational examples of the levels of path spaces and Borel constructions, including biquotient spaces and Davis-Januszkiewicz spaces, are presented. We also show that the chain type level of the homotopy fibre of a map is greater than the E-category in the sense of Kahl, which is an algebraic approximation of the Lusternik-Schnirelmann category of the map. The inequality fits between the grade and the projective dimension of the cohomology of the homotopy fibre.
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