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Title Transcription
コテン グン ノ ドウヘン ホモトピー グン ニツイテ
Title Alternative (English)
Equivariant Homotopy Groups of Classical Groups
File
language
eng
Author
Matsunaga, Hiromichi
Description
In [4] we have studied the surjectivity of the forgetful homomorphism f(G, X) : K_G(X)→ K(X). The homomorphism gives informations about lifting actions on stabl vector bundles. One of the purpose of this paper is to study lifting actions on vector bundles and give actions explicitly for geometrical uses, for example, equivariant Hopf constructions and a lifting problem for other spaces than the spheres.
In section I we shall give a criterion for the existence of lifting actions which is obtained by G. Bredon's work [2]. Section 2 consists of results obtained by J. Folkinan's theorems [3], and Proposition 3 in [5]. Moreover we shall prove the equivariance for representatives of of generators of the groups _<π3>(SO(4)) and _<π7>(SO(8)). In section 3 we shall prove the equivariance of Bott maps [1], which present us various constructions of equivariant maps. In the last section we shall apply results in preceding sections and obtain a non existence theorem, equivanant Hopf constructions and a lifting property on complex plane bundles over the complex projective plane.
Journal Title
Memoirs of the Faculty of Science, Shimane University
Volume
21
Start Page
21
End Page
30
ISSN
03879925
Published Date
1987-12-25
NCID
AN00108106
Publisher
島根大学理学部
Publisher Aalternative
The Faculty of Science, Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Science and Engineering
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