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Universal phantom maps out of loop spaces*

Published online by Cambridge University Press:  11 July 2007

K. Iriye
K. Iriye
Affiliation:
Department of Applied Mathematics, Osaka Women's University, Sakai, Osaka 590-0035, Japan (kiriye@appmath.osaka-wu.ac.jp)
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Abstract

We consider the universal phantom map out of a non-finite loop space. First we obtain a necessary and sufficient condition for the universal phantom map out of ΩG for a simply connected compact Lie group G to be essential. Next we prove that the universal phantom map out of ΩkX is essential for all k ≥ 2 if X is a simply connected non-contractible finite CW-complex. Ingredients in the proof are the Browder's ∞-implication argument and the Eilenberg–Moore spectral sequence.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 2 , April 2000 , pp. 313 - 333
Copyright
Copyright © Royal Society of Edinburgh 2000

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References

* Dedicated to the memory of Professor Katsuo Kawakubo.