Higher associativity of Moore spectra

TL;DR

This paper establishes a lower bound on the parameter for Moore spectra to be n-fold associative, linking algebraic properties to stable homotopy groups of spheres.

Contribution

It provides a new lower bound on the associativity level of Moore spectra based on stable homotopy groups, advancing understanding of their algebraic structure.

Findings

Derived a lower bound depending on stable homotopy groups

Connected associativity properties to homotopy-theoretic invariants

Enhanced understanding of Moore spectra's algebraic behavior

Abstract

The Moore spectrum $\mathrm{M}_p(i)$ is the cofiber of the $p^{i}$ map on the sphere spectrum. For a fixed $p$ and $n$, we find a lower bound on $i$ for which $\mathrm{M}_p(i)$ is guaranteed to be $n$-fold associative. This bound depends on the stable homotopy groups of spheres.