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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ \boldsymbol{\pi_*}$-kernels of Lie groups


Author: Ken-ichi Maruyama
Journal: Trans. Amer. Math. Soc. 358 (2006), 2335-2351
MSC (2000): Primary 55Q05; Secondary 55P10, 57T20
Published electronically: January 27, 2006
MathSciNet review: 2204034
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a filtration on the group of homotopy classes of self maps of a compact Lie group associated with homotopy groups. We determine these filtrations of $ SU(3)$ and $ Sp(2)$ completely. We introduce two natural invariants $ lz_p(X)$ and $ sz_p(X)$ defined by the filtration, where $ p$ is a prime number, and compute the invariants for simple Lie groups in the cases where Lie groups are $ p$-regular or quasi $ p$-regular. We apply our results to the groups of self homotopy equivalences.


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Additional Information

Ken-ichi Maruyama
Affiliation: Department of Mathematics, Faculty of Education, Chiba University, Yayoicho, Chiba, Japan
Email: maruyama@faculty.chiba-u.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04199-7
PII: S 0002-9947(06)04199-7
Keywords: Self homotopy sets, Lie groups, stability, length
Received by editor(s): July 16, 2003
Published electronically: January 27, 2006
Additional Notes: This research was partially supported by Grant-in-Aid for Scientific Research (14540063), The Ministry of Education, Culture, Sports, Science and Technology, Japan
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.