Decompositions of looped co-H-spaces and applications

2010/11/05 by J. Grbi, Grbic, Jelena, Stephen Theriault +3
Mathematics · #05E05 #20C20 #52C35 #55P35 #55P45 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1011.1414

openalex publication_date 2010/11/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Higher Whitehead products in toric topology
• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

Related

• Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space
• Loop spaces and homotopy operations
• Loop Space Decompositions of Connected Sums and Applications to the Vigué-Poirrier Conjecture
• An Interpolation between Homology and Stable Homotopy
• The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations