Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces
Algebraic Topology
2013-01-01 v1
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.
Keywords
Cite
@article{arxiv.1111.4669,
title = {Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces},
author = {Jesus Gonzalez and Maurilio Velasco and W. Stephen Wilson},
journal= {arXiv preprint arXiv:1111.4669},
year = {2013}
}
Comments
32 pages