Document Type

Article

Publication Date

1-27-2025

Abstract

Whitehead products and natural infinite sums are prominent in the higher homotopy groups of the n-dimensional infinite earring space En" role="presentation"> and other locally complicated Peano continua. In this paper, we derive general identities for how these operations interact with each other. As an application, we consider a shrinking wedge of finite (n−1)" role="presentation">-connected CW-complexes and compute the infinite-sum closure W2n−1(X)" role="presentation"> of the set of Whitehead products [α,β]" role="presentation"> in π2n−1(X)" role="presentation"> where α,β∈πn(X)" role="presentation"> are represented in respective sub-wedges that meet only at the basepoint. In particular, we show that W2n−1(X)" role="presentation"> is canonically isomorphic to ∏j=1∞(πn(Xj)⊗∏k>jπn(Xk))" role="presentation">. The insight provided by this computation motivates a conjecture about the isomorphism type of the elusive groups π2n−1(En)" role="presentation">, n≥2" role="presentation">.

Publication Title

Topology and its Applications

ISSN

0166-8641,

Publisher

ScienceDirect

Volume

Volume 362

DOI

10.1016/j.topol.2025.109232

Download

Share

COinS