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Weighted cup-length calculations in singular cohomology led Farber and Grantin 2008 to general lower bounds for the topological complexity of lens spaces.We replace singular cohomology by K-theory, and weighted cup-length argumentsby considerations with biequivariant maps on spheres to improve onFarber-Grant's bounds by arbitrarily large amounts. Our calculations are basedon the identification of key elements conjectured to generate the annihilatorideal of the toral bottom class in the ku-homology of the classifying space ofa rank-2 abelian 2-group.

Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces