Bounds for higher topological complexity of real projective space implied by BP

TL;DR

This paper employs Brown-Peterson cohomology to derive significantly improved lower bounds for the higher topological complexity of real projective spaces, surpassing those obtained via standard mod-2 cohomology.

Contribution

It introduces a novel application of Brown-Peterson cohomology to establish stronger bounds for TC_k(RP^n).

Findings

Lower bounds for TC_k(RP^n) are enhanced using BP cohomology.

Results often outperform bounds from mod-2 cohomology.

Provides new insights into the topological complexity of real projective spaces.

Abstract

We use Brown-Peterson cohomology to obtain lower bounds for the higher topological complexity, TC_k(RP^n), of real projective spaces, which are often much stronger than those implied by ordinary mod-2 cohomology.