Multiaxial actions on manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1978
|
| Series: | Lecture notes in mathematics
643 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 141 S. |
| ISBN: | 3540086676 0387086676 |
Staff View
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| 100 | 1 | |a Davis, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multiaxial actions on manifolds |c Michael Davis |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1978 | |
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Record in the Search Index
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| adam_text | CONTENTS
page
0. Introduction 1
1. Some History (Lecture 1) . 3
A. Actions modeled on lp 3
1. The example of Montgomery and Samelson 3
2. Wu-yi Hsiang s thesis 4
B. Actions modeled on 2P 11
1. Bredon s examples 11
2. The classification theorem of the Hsiangs and
Janich for actions with two types of orbits 12
3. Knot manifolds 13
4. U(n) and Sp(n) knot manifolds 15
References 16
II. Some Preliminary Facts Concerning the Linear Model and
Its Orbit Space (Lecture 2). 18
A. The linear representation kp 18
B. The orbit space of M(n,k) 20
III.The Normal Bundles of the Strata and Twist Invariants 24
A. The equivariant normal bundle of a stratum 24
B. The mysterious twist invariants 2 5
C. The classification of biaxial actions without fixed
points 29
D. Remarks concerning the general classification theorem 31
References 32
IV. A Structure Theorem for Multiaxial Actions and Some of
its Consequences (Lecture 3). 34
A. The Structure Theorem 34
VI
1. The twist invariants of the linear model 34
2. Stratified maps 41
3. The Main Theorem 41
B. The pullback construction and the Covering Homotopy
Theorem 46
C. A Classification Theorem 50
D. Applications to knot manifolds and other biaxial
actions 52
E. Applications to triaxial actions without fixed
points 56
F. Some counterexamples 60
G. Further classification theorems 63
References 64
V. Actions on Spheres (Lecture 4). 66
A. The homology of the strata 67
1. The U(n) and Sp(n) cases 67
2. The 0(n) case 69
B. An application of Borel s formula 73
C. The bundle of principal orbits of a k-axial action
on a sphere is trivial, if n k. 76
References 84
VI. Concordance Classes of Actions on Spheres (Lecture 5). 85
A. The plan of attack 87
B. Multiaxial actions bound 90
C. The calculation of 9 (k^n^m) 96
References 102
Appendix 1: Biaxial actions of SO (3), G and SU(3) on
homotopy spheres 103
References 116
Appendix 2: The homology of the strata in the 0(n) case 117
|
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| genre | Multiaxiale Aktionen gnd Multiaxiale Operationen gnd |
| genre_facet | Multiaxiale Aktionen Multiaxiale Operationen |
| id | DE-604.BV002251142 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:47Z |
| institution | BVB |
| isbn | 3540086676 0387086676 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001479232 |
| oclc_num | 612120908 |
| open_access_boolean | |
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| physical | VI, 141 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Davis, Michael Verfasser aut Multiaxial actions on manifolds Michael Davis Berlin [u.a.] Springer 1978 VI, 141 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 643 Groupes de Lie Groupes topologiques de transformation Groupes topologiques de transformations - Congrès ram Lie, Groupes de - Congrès ram Variétés (Mathématiques) Variétés (mathématiques) - Congrès ram Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Multiaxiale Aktionen gnd rswk-swf Multiaxiale Operationen gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Lie-Gruppe (DE-588)4035695-4 s Multiaxiale Operationen f DE-604 Multiaxiale Aktionen f Lecture notes in mathematics 643 (DE-604)BV000676446 643 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001479232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davis, Michael Multiaxial actions on manifolds Lecture notes in mathematics Groupes de Lie Groupes topologiques de transformation Groupes topologiques de transformations - Congrès ram Lie, Groupes de - Congrès ram Variétés (Mathématiques) Variétés (mathématiques) - Congrès ram Lie-Gruppe (DE-588)4035695-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4037379-4 |
| title | Multiaxial actions on manifolds |
| title_auth | Multiaxial actions on manifolds |
| title_exact_search | Multiaxial actions on manifolds |
| title_full | Multiaxial actions on manifolds Michael Davis |
| title_fullStr | Multiaxial actions on manifolds Michael Davis |
| title_full_unstemmed | Multiaxial actions on manifolds Michael Davis |
| title_short | Multiaxial actions on manifolds |
| title_sort | multiaxial actions on manifolds |
| topic | Groupes de Lie Groupes topologiques de transformation Groupes topologiques de transformations - Congrès ram Lie, Groupes de - Congrès ram Variétés (Mathématiques) Variétés (mathématiques) - Congrès ram Lie-Gruppe (DE-588)4035695-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Groupes de Lie Groupes topologiques de transformation Groupes topologiques de transformations - Congrès Lie, Groupes de - Congrès Variétés (Mathématiques) Variétés (mathématiques) - Congrès Lie-Gruppe Mannigfaltigkeit Multiaxiale Aktionen Multiaxiale Operationen |
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