Topological complexity of 2-torsion lens spaces and ku-(co)homology

TL;DR

This paper uses ku-cohomology to establish lower bounds on the topological complexity of 2-torsion lens spaces and provides a detailed algebraic analysis of their ku-homology tensor products.

Contribution

It offers an almost-complete description of the ku-homology tensor product for infinite mod 2^e lens spaces, proving Gonzalez's conjecture on the annihilator ideal.

Findings

Lower bounds for topological complexity of 2-torsion lens spaces

Complete description of ku-homology tensor products

Proof of Gonzalez's conjecture on annihilator ideal

Abstract

We use ku-cohomology to determine lower bounds for the topological complexity of 2-torsion lens spaces. In the process, we give an almost-complete description of the tensor product of two copies of the ku-homology of infinite mod 2^e lens space, proving a conjecture of Gonzalez about the annihilator ideal of the bottom class. Our proof involves an elaborate row reduction of presentation matrices of arbitrary size.