**Mathematical Surveys and Monographs**

Volume: 166;
2010;
396 pp;
Hardcover

MSC: Primary 55; 57;
Secondary 53; 58

Print ISBN: 978-0-8218-5231-6

Product Code: SURV/166

List Price: $104.00

Individual Member Price: $83.20

**Electronic ISBN: 978-1-4704-1393-4
Product Code: SURV/166.E**

List Price: $104.00

Individual Member Price: $83.20

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#### Supplemental Materials

# Seifert Fiberings

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*Kyung Bai Lee; Frank Raymond*

Seifert fiberings extend the notion of fiber bundle mappings by allowing some of the fibers to be singular. Away from the singular fibers, the fibering is an ordinary bundle with fiber a fixed homogeneous space. The singular fibers are quotients of this homogeneous space by distinguished groups of homeomorphisms. These fiberings are ubiquitous and important in mathematics. This book describes in a unified way their structure, how they arise, and how they are classified and used in applications. Manifolds possessing such fiber structures are discussed and range from the classical three-dimensional Seifert manifolds to higher dimensional analogues encompassing, for example, flat manifolds, infra-nil-manifolds, space forms, and their moduli spaces. The necessary tools not covered in basic graduate courses are treated in considerable detail. These include transformation groups, cohomology of groups, and needed Lie theory. Inclusion of the Bieberbach theorems, existence, uniqueness, and rigidity of Seifert fiberings, aspherical manifolds, symmetric spaces, toral rank of spherical space forms, equivariant cohomology, polynomial structures on solv-manifolds, fixed point theory, and other examples, exercises and applications attest to the breadth of these fiberings. This is the first time the scattered literature on singular fiberings is brought together in a unified approach. The new methods and tools employed should be valuable to researchers and students interested in geometry and topology.

#### Table of Contents

# Table of Contents

## Seifert Fiberings

- Contents ix10 free
- Preface xiii14 free
- Chapter 1. Transformation Groups 122 free
- Chapter 2. Group Actions and the Fundamental Group 2344
- Chapter 3. Actions of Compact Lie Groups on Manifolds 4768
- Chapter 4. Definition of Seifert Fibering 6990
- Chapter 5. Group Cohomology 95116
- Chapter 6. Lie Groups 109130
- Chapter 7. Seifert Fiber Space Construction for $G \times W$ 119140
- Chapter 8. Generalization of Bieberbach's Theorems 139160
- Chapter 9. Seifert Manifolds with $\Gamma\ G/K$-Fiber 159180
- Chapter 10. Locally Injective Seifert Fiberings with Torus Fibers 179200
- Chapter 11. Applications 205226
- Chapter 12. Seifert Fiberings with Compact Connected $Q$ 269290
- Chapter 13. Deformation Spaces 283304
- Chapter 14. $S^1$-actions on 3-dimensional Manifolds 299320
- Chapter 15. Classification of Seifert 3-manifolds via equivariant cohomology 353374
- Bibliography 383404
- Index 393414 free

#### Readership

Graduate students and research mathematicians interested in topology (transformation groups, manifolds, singular fiberings, and differential geometry).