关于具有交换基本群的流形的拓扑复杂性
On the topological complexity of manifolds with abelian fundamental group
摘要：
给出了具有交换基本群的闭流形$M$的拓扑复杂性非极大的条件，并通过实例证明了所给条件的正确性.推广了Costa和Farber关于具有小基本群的空间的拓扑复杂性的结果.放松交换性条件的基本群，我们还推广了Dranishnikov的结果的Lusternik-Schnirelmann范畴的上纤维的对角映射$Δ: M \to M \times M$的不可定向曲面通过建立非极大性的这一不变量的一大类流形。
英文摘要：
We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on the topological complexity of spaces with small fundamental group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik-Schnirelmann category of the cofibre of the diagonal map $Δ: M \to M \times M$ for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.
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