Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T20:34:06.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Unstable atomicity of ΩSpin(r)

Published online by Cambridge University Press:  14 November 2011

Zafer Mahmud
Zafer Mahmud
Affiliation:
Mathematics Department, Kuwait University, P.O. Box 5969, Safat, Kuwait
Get access Rights & Permissions [Opens in a new window]

Synopsis

We determine the homomorphism induced, in Z2-cohomology, by a map f: ΩSpin(r) → ΩSpin(r). As a corollary we show that ΩSpin(r), r ≧ 9 is 2-atomic, where a space X is 2-atomic if any map f: X ≧X is either a mod 2 homotopy equivalence or f*: H*(X, Z2) → H*(X, Z2) is nilpotent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 1-2 , 1989 , pp. 53 - 69
Copyright
Copyright © Royal Society of Edinburgh 1989

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

1Atiyah, M. F.. Power operations in K-theory. Quart J. Math. 17 (1966), 165–193.CrossRefGoogle Scholar
2Bott, R.. The space of loops on a Lie group. Michigan Math. J. 5 (1958), 35–61.CrossRefGoogle Scholar
3Bourbaki, N.. Groupes et algebres de Lie. Chapter 9 (Paris: Masson, 1982).Google Scholar
4Clarke, F.. On the K-theory of the loop space of a Lie group. Proc. Camb. Phil. Soc. 76 (1974), 1–20.CrossRefGoogle Scholar
5Hubbuck, J. R.. Unstable atomicity and Loop Spaces on a Lie group. Math. Z. (to appear).Google Scholar
6Riordan, J.. Combinatorial Identities (New York: Wiley, 1968).Google Scholar