Unstable higher Toda brackets III

TL;DR

This paper introduces a new inductive definition of unstable higher Toda brackets for spaces with base points and explores their stable counterparts, advancing the understanding of algebraic topology structures.

Contribution

It provides the first systematic inductive framework for unstable n-fold Toda brackets and their stable versions in the category of pointed spaces.

Findings

Defined unstable n-fold Toda brackets for all n>2

Established a method to define stable Toda brackets

Enhanced the algebraic understanding of topological space structures

Abstract

We define inductively unstable n-fold Toda brackets for every n>2 in the category of spaces with base points, and then define stable ones.