Title Transcription  キュウメン ジョウノ キュウメン ソク エノ S1 サヨウ

Title Alternative  S^<1>Actions on Sphere Bundles over Spheres

File  
language 
eng

Author 
Matsunaga, Hiromichi

Description  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^kbundlles 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^3bundles over S^4 and S^7bundles over S^8. By means of reductions of structure groups, we can give S^1actions on S^kbundles over S^n for k≧n. Using wellknowm results from the homotopy theory of spheres and rotation groups, we construct actions on S^kbundles over S^n for k＜n≦8 in section 2. In the last section, we construct actions on S^<4s1>_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(2s1)!/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. 
Journal Title 
Memoirs of the Faculty of Science, Shimane University

Volume  15

Start Page  9

End Page  16

ISSN  03879925

Published Date  19811220

NCID  AN00108106

Publisher  島根大学理学部

Publisher Aalternative  The Faculty of Science, Shimane University

NII Type 
Departmental Bulletin Paper

OAIPMH Set 
Faculty of Science and Engineering
