Decompositions of looped co-H-spaces

We prove two homotopy decomposition theorems for the loops on simply-connected co-H-spaces, including a generalization of the Hilton-Milnor Theorem. Several examples are given.

[1]  Jie Wu,et al.  Suspension splittings and James–Hopf invariants , 2014, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[2]  Jie Wu,et al.  Functorial homotopy decompositions of looped co-H spaces , 2011 .

[3]  Jie Wu The functor Amin for (p − 1)-cell complexes and EHP sequences , 2010, 1002.0929.

[4]  J. Wu,et al.  Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras , 2010, Proceedings of the Edinburgh Mathematical Society.

[5]  Jie Wu,et al.  The decomposition of the loop space of the mod $2$ Moore space , 2008 .

[6]  S. Theriault,et al.  Functorial Decompositions of Looped Coassociative Co-H Spaces , 2006, Canadian Journal of Mathematics.

[7]  Jie Wu,et al.  The functor Amin on p-local spaces , 2006 .

[8]  Jie Wu,et al.  On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions , 2000 .

[9]  A. Zabrodsky Some relations in the mod 3 cohomology ofH-spaces , 1979 .

[10]  M. Mimura,et al.  Localization of CW-complexes and its applications , 1971 .

[11]  G. J. Porter The Homotopy Groups of Wedges of Suspensions , 1966 .

[12]  I. Berstein On co-groups in the category of graded algebras , 1965 .

[13]  I. Berstein A note on spaces with non-associative co-multiplication , 1964, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  I. James REDUCED PRODUCT SPACES , 1955 .

[15]  W. J.,et al.  MODULE STRUCTURE ON LIE POWERS AND NATURAL COALGEBRA-SPLIT SUB HOPF ALGEBRAS OF TENSOR ALGEBRAS , 2009 .

[16]  F. Cohen,et al.  A construction of p-local H-spaces , 1984 .

[17]  A. Zabrodsky,et al.  Torsion free mod p H-spaces of low rank , 1979 .

[18]  J. C. Moore,et al.  Torsion in Homotopy Groups , 1979 .