Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-20T01:08:54.570Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

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.

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

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

* Dedicated to the memory of Professor Katsuo Kawakubo.