Decompositions of looped co-H-spaces and applications

TL;DR

This paper presents new homotopy decomposition theorems for loops on co-H-spaces, generalizing classical results and applying them to diverse areas like algebra, topology, and combinatorics.

Contribution

It introduces two new decomposition theorems for looped co-H-spaces, including a broad generalization of the Hilton-Milnor Theorem.

Findings

Established homotopy decompositions for loops on co-H-spaces

Generalized the Hilton-Milnor Theorem

Applied results to algebra, topology, and combinatorics

Abstract

We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topology, and the study of quasi-symmetric functions.