**Contemporary Mathematics**

Volume: 36;
1985;
568 pp;
Softcover

MSC: Primary 57;
Secondary 55

Print ISBN: 978-0-8218-5038-1

Product Code: CONM/36

List Price: $74.00

Individual Member Price: $59.20

**Electronic ISBN: 978-0-8218-7621-3
Product Code: CONM/36.E**

List Price: $74.00

Individual Member Price: $59.20

# Group Actions on Manifolds

Share this page *Edited by *
*Reinhard Schultz*

Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable.

The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado. A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgment of the work and influence of D. Montgomery on the subject.

#### Table of Contents

# Table of Contents

## Group Actions on Manifolds

- Contents vii8 free
- Introduction ix10 free
- Summary of Program xi12 free
- List of Participants xv16 free
- The work and influence of Deane Montgomery 118 free
- Bibliography of Deane Montgomery 1330
- Homotopy-theoretic techniques and applications: 1734
- Homological methods and machinery: 107124
- A family of unusual torus group actions 107124
- For G = s1 there is no G-Chern character 113130
- Equivariant frameability of homotopy linear s1 actions on spheres 119136
- Action maps on equivariant function spaces and applications to PL bordism 123140
- Borsuk-Ulam theorems for prime periodic transformation groups 135152
- On equivariant maps of Stiefel manifolds 145162

- Applications of surgery and geometric topology: 151168
- Representations at fixed points 151168
- Transformation groups and fixed point data 159176
- Lectures on transformation groups and Smith equivalence 191208
- Transformation groups and exotic spheres 243260
- Constructions of group actions: A survey of recent developments 269286
- Concordance of group actions on spheres 299316
- Induction in equivariant K-theory and s-Smith equivalence of representations 311328
- Smith equivalent representations of generalized quaternion groups 317334
- s-Smith equivalent representations for finite abelian groups 323340
- Isotropy representations of nonabelian finite group actions 331348

- Low-dimensional topology and transformation groups: 339356
- Homogeneous spaces and seifert fiberings: 367384
- Transformation groups and differential geometry: 489506
- Problems: 513530
- Problems submitted to the A.M.S. Summer Research Conference on Group Actions 513530
- Introduction 513530
- 1. Realization questions 516533
- 2. Inductive existence and classification questions 522539
- 3. Absolute existence questions 527544
- 4. General structure questions 530547
- 5. Questions involving equivariant algebraic topology 535552
- 6. Questions on group actions and low-dimensional topology. 543560
- 7. Problems concerning smooth actions on spheres 546563
- 8. Problems concerning actions on spherelike spaces 553570
- 9. Group actions and topological singularities 559576
- 10. Topological similarity of representations 562579
- 11. Transformation groups and geometry 564581