Symmetricity of the Whitehead element

Hiroshima Mathematical Journal Volume 27 Issue 2 Page 221-228 published_at 1997-07
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Title ( eng )
Symmetricity of the Whitehead element
Creator
Kawamoto Yusuke
Source Title
Hiroshima Mathematical Journal
Volume 27
Issue 2
Start Page 221
End Page 228
Abstract
We study the symmetricity of the Whitehead element w_n ∊ π_<2np-3> (S^<2n-1>) for an odd prime p. It is shown that w_n considered as a map S^<2np-3> → S^<2n-1> factors through the p-fold covering map σ : S^<2np-3> → L^<2np-3> only when n is a power of p, and that w_<p^i>, actually factors through σ if 0 ≤ i ≤ 4. This is some of an odd prime version of the results of Randall and Lin for the projectivity of the Whitehead product [l_<2n-1>, l_<2n-1>] ∊ π_<4n-3>(S^<2n-1>).
Keywords
Whitehead element
symmetric
lens space
NDC
Mathematics [ 410 ]
Language
eng
Resource Type departmental bulletin paper
Publisher
Department of Mathematics, Faculty of Science, Hiroshima University
Date of Issued 1997-07
Publish Type Version of Record
Access Rights open access
Source Identifier
[ISSN] 0018-2079
[NCID] AA00664323