From $K(n+1)_*(X)$ to $K(n)_*(X)$
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- by Norihiko Minami PDF
- Proc. Amer. Math. Soc. 130 (2002), 1557-1562 Request permission
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 $S(X,K(n)) = \{ m \in \mathbb {Z}/q\mathbb {Z} \mid \bigoplus _{d \equiv m \bmod q}\ K(n)^d \neq 0 \}$ 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.
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1557-1562
- MSC (2000): Primary 55N15, 55N20, 55N22; Secondary 55Q51, 55R35
- DOI: https://doi.org/10.1090/S0002-9939-01-06374-2
- MathSciNet review: 1879983