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arXiv · 1111.4669

Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces

Jesus Gonzalez·Maurilio Velasco·W. Stephen Wilson
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Abstract

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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Jesus Gonzalez, Maurilio Velasco, W. Stephen Wilson. 2011-11-20. Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces. https://doi.org/10.1142/s0219199712500514

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