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タイトルヨミ
キュウメン ジョウノ キュウメン ソク エノ S1- サヨウ
日本語以外のタイトル
S^<1->Actions on Sphere Bundles over Spheres
ファイル
言語
英語
著者
松永 弘道
内容記述(抄録等)
In this paper, we shall construct compact Lie group actions on total spaces of orientable sphere bundles over spheres. All actions considered in this paper preserve bundle structures, that is, each element of groups gives a bundle map. The author intends to construct actions on all sphere bundles over S^n for n≦8. For n > 8, actions on S^k-bundlles over S^n are given for the case of k ≧ n and other particular n, k. Thus we can conclude that these bundle spaces have positive degrees of symmetry.
In section 1, we construct actions on S^3-bundles over S^4 and S^7-bundles over S^8. By means of reductions of structure groups, we can give S^1-actions on S^k-bundles over S^n for k≧n. Using well-knowm results from the homotopy theory of spheres and rotation groups, we construct actions on S^k-bundles over S^n for k<n≦8 in section 2. In the last section, we construct actions on S^<4s-1>_bundles over S^<4s> of types B_<l,o>, B_<o,l> and B,εk m k, where ε=1 if s is odd, ε=2 if s is even, m-(2s-1)!/2 and k is an integer.
The technique used in this paper is quite homotopical and actually elementary. Our results are essentially due to the computatioms of M. A. Kervaire, [3] and we shall use it frequently in this paper.
掲載誌名
島根大学理学部紀要
15
開始ページ
9
終了ページ
16
ISSN
03879925
発行日
1981-12-20
NCID
AN00108106
出版者
島根大学理学部
出版者別表記
The Faculty of Science, Shimane University
資料タイプ
紀要論文
部局
総合理工学部
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