**Memoirs of the American Mathematical Society**

1996;
93 pp;
Softcover

MSC: Primary 57;
Secondary 22

Print ISBN: 978-0-8218-0409-4

Product Code: MEMO/119/569

List Price: $44.00

Individual Member Price: $26.40

**Electronic ISBN: 978-1-4704-0148-1
Product Code: MEMO/119/569.E**

List Price: $44.00

Individual Member Price: $26.40

# Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I

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*Eldar Straume*

In the study of Lie transformation groups on classical
space forms, one of the most exciting features is the existence of
nonlinear or “exotic” actions. Among the many unsolved
problems, the classification of G-spheres with 2-dimensional orbit space
has a prominent place. The main purpose of this monograph is to describe
the beginnings of a program to the complete solution of this problem.
One major feature of the author's approach is the effectiveness of
the geometric weight system, which was introduced by Wu-Yi Hsiang
around 1970, as a book-keeping method for orbit structural data.

Features:

- Complete tables of compact connected linear groups of cohomogeneity \(< 3\).
- Geometric weight systems techniques.
- Complete classification of G-spheres of cohomogeneity one.
- Weight classification of G-spheres of cohomogeneity two, the crucial step of the complete classification for cohomogeneity two.

#### Table of Contents

# Table of Contents

## Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I

- Table of Contents v6 free
- Introduction 18 free
- Chapter I: Linear groups of cohomogeneity < 4 714 free
- Chapter II: Determination of weight patterns 1522
- Chapter III: Fixed point results of P.A.Smith type 7178
- Chapter IV: Classification of compact connected Lie transformation groups on spheres with cohomogeneity one 7582
- Appendix: Table I, II, III; c(<Φ) ≤ 3 8289
- References 9198

#### Readership

Graduate students and research mathematicians in topology/geometry, invariant theory, theoretical physics and physicists who apply Lie theory.