Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

From $K(n+1)_*(X)$ to $K(n)_*(X)$


Author: Norihiko Minami
Journal: Proc. Amer. Math. Soc. 130 (2002), 1557-1562
MSC (2000): Primary 55N15, 55N20, 55N22; Secondary 55Q51, 55R35
Published electronically: October 12, 2001
MathSciNet review: 1879983
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a space of finite type. Set $q=2(p-1)$ as usual, and define the mod $q$ support of $K(n)^*(X)$ by $ S(X,K(n)) = \{ m \in { \mathbb Z}/q{ \mathbb Z}\mid \bigoplus_{d \equiv m \operatorname{mod}q} K(n)^d \neq 0 \} $ for $n>0.$ Call $K(n)^*(X)$sparse if there is no $m \in { \mathbb Z}/q{ \mathbb Z}$ with $ m, m+1 \in S(X,K(n)). $

Then we show the relation $ S(X,K(n)) \subseteqq S(X,K(n+1)) $ for any finite type space $X$ with $K(n+1)^*(X)$ being sparse.

As a special case, we have $ K(n+1)^{odd}(X) = 0 \Longrightarrow K(n)^{odd}(X) = 0, $ and the main theorem of Ravenel, Wilson and Yagita is also generalized in terms of the mod $q$ support.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55N15, 55N20, 55N22, 55Q51, 55R35

Retrieve articles in all journals with MSC (2000): 55N15, 55N20, 55N22, 55Q51, 55R35


Additional Information

Norihiko Minami
Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya 466-8555, Japan
Email: norihiko@math.kyy.nitech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06374-2
PII: S 0002-9939(01)06374-2
Keywords: Morava $K$-theory, unstable homotopy theory, classifying space
Received by editor(s): November 20, 2000
Published electronically: October 12, 2001
Additional Notes: This research was partially supported by Grant-in-Aid for Scientific Research No. 11640072, Japan Society for the Promotion of Science
Communicated by: Ralph Cohen
Article copyright: © Copyright 2001 American Mathematical Society