Seifert fiberings / Kyung Bai Lee, Frank Raymond.

Format:

Book

Author/Creator:

Lee, Kyung Bai, 1943- author.

Raymond, Frank, 1932- author.

Series:

Mathematical surveys and monographs ; v. 166.

Mathematical surveys and monographs ; volume 166

Language:

English

Subjects (All):

Fiberings (Mathematics).

Complex manifolds.

Physical Description:

1 online resource (418 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2010]

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Preface""; ""Chapter 1. Transformation Groups""; ""Chapter 2. Group Actions and the Fundamental Group""; ""Chapter 3. Actions of Compact Lie Groups on Manifolds""; ""Chapter 4. Definition of Seifert Fibering""; ""Chapter 5. Group Cohomology""; ""Chapter 6. Lie Groups""; ""Chapter 7. Seifert Fiber Space Construction for G \times W""; ""Chapter 8. Generalization of Bieberbach's Theorems""; ""Chapter 9. Seifert Manifolds with \Gamma\ G/K-Fiber""; ""Chapter 10. Locally Injective Seifert Fiberings with Torus Fibers""; ""Chapter 11. Applications""

""Chapter 12. Seifert Fiberings with Compact Connected Q""""Chapter 13. Deformation Spaces""; ""Chapter 14. S^1-actions on 3-dimensional Manifolds""; ""Chapter 15. Classification of Seifert 3-manifolds via equivariant cohomology""; ""Bibliography""; ""Index""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1393-0