Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces

Details Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces

2011-11-20

arxiv.org/abs/1111.4669v1

Mathematics

Algebraic Topology

32 pages

Scientific paper

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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