球面上的双等变映射与透镜空间的拓扑复杂性
Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces
摘要：
奇异上同调的加权杯长计算使法伯和格兰特在2008年得到了透镜空间拓扑复杂度的一般下界。我们取代奇异上同调的K-理论，加权杯长参数的考虑与双等变映射的领域，以提高法伯-格兰特的界限任意大的金额。我们的计算是基于识别的关键元素，所述关键元素是为了在秩-2交换2-群的分类空间的ku-同调中生成toral底类的零化子理想而确定的。
英文摘要：
Weighted cup-length calculations in singular cohomology led Farber and Grant in 2008 to general lower bounds for the topological complexity of lens spaces. We replace singular cohomology by K-theory, and weighted cup-length arguments by considerations with biequivariant maps on spheres to improve on Farber-Grant's bounds by arbitrarily large amounts. Our calculations are based on the identification of key elements conjectured to generate the annihilator ideal of the toral bottom class in the ku-homology of the classifying space of a rank-2 abelian 2-group.
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