Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-27T02:40:04.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Associative h-spaces and algebras

Published online by Cambridge University Press:  24 October 2008

John W. Rutter
John W. Rutter
Affiliation:
University of Liverpool
Get access Rights & Permissions [Opens in a new window]

Extract

1. Ganea has shown (Theorem 2·2 of (2)) that h-cogroup structures on a CW space coincide, in the homotopy category, with coalgebra structures defined with respect to the cotriple determined by SΩ. The construction used by Ganea to prove this does not dualize. It seems possible moreover that the dual statement is false. In this note I show, using the results of (4), that, for suitable spaces, there is a surjection from the set of algebra structures defined with respect to the triple determined by ΩS to the set of h-group structures, and I construct a right inverse for this surjection.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 67 - 69
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Eilenberg, S. and Moore, J. C.Adjoint functors and triples, Illinois J. Math. 9 (1965), 381–398.CrossRefGoogle Scholar
(2)Ganea, T.Cogroups and suspensions. Invent. Math. 9 (1970), 185–197.CrossRefGoogle Scholar
(3)James, I. M.Multiplications on spheres (II). Trans. Amer. Math. Soc. 84 (1957), 545–558.Google Scholar
(4)Rutter, J. W.The loops on the suspension of a space with multiplication. Math. Ann. 214 (1975), 81–94.CrossRefGoogle Scholar