The infinitary n-cube shuffle

TL;DR

This paper formalizes the concept of infinite commutativity in higher homotopy groups and extends a complex method for rearranging infinite configurations of n-cubes within a unit n-cube.

Contribution

It simplifies and extends the existing procedure for constructing homotopies that rearrange infinite configurations of disjoint n-cubes.

Findings

Formalization of infinite commutativity in higher homotopy groups

Extension of Eda and Kawamura's procedure for homotopy construction

Simplified method for rearranging infinite n-cube configurations

Abstract

In this paper, we formalize the sense in which higher homotopy groups are "infinitely commutative." In particular, we both simplify and extend the highly technical procedure, due to Eda and Kawamura, for constructing homotopies that isotopically rearrange infinite configurations of disjoint $n$-cubes within the unit $n$-cube.