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Seifert Fiberings

Kyung Bai Lee University of Oklahoma, Norman, OK
Frank Raymond University of Michigan, Ann Arbor, MI
Available Formats:
Hardcover ISBN: 978-0-8218-5231-6
Product Code: SURV/166
List Price: $111.00 MAA Member Price:$99.90
AMS Member Price: $88.80 Electronic ISBN: 978-1-4704-1393-4 Product Code: SURV/166.E List Price:$104.00
MAA Member Price: $93.60 AMS Member Price:$83.20
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List Price: $166.50 MAA Member Price:$149.85
AMS Member Price: $133.20 Click above image for expanded view Seifert Fiberings Kyung Bai Lee University of Oklahoma, Norman, OK Frank Raymond University of Michigan, Ann Arbor, MI Available Formats:  Hardcover ISBN: 978-0-8218-5231-6 Product Code: SURV/166  List Price:$111.00 MAA Member Price: $99.90 AMS Member Price:$88.80
 Electronic ISBN: 978-1-4704-1393-4 Product Code: SURV/166.E
 List Price: $104.00 MAA Member Price:$93.60 AMS Member Price: $83.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$166.50 MAA Member Price: $149.85 AMS Member Price:$133.20
• Book Details

Mathematical Surveys and Monographs
Volume: 1662010; 396 pp
MSC: Primary 55; 57; Secondary 53; 58;

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.

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

• Chapters
• 1. Transformation groups
• 2. Group actions and the fundamental group
• 3. Actions of compact Lie groups on manifolds
• 4. Definition of Seifert fibering
• 5. Group cohomology
• 6. Lie groups
• 7. Seifert fiber space construction for $G\times W$
• 8. Generalization of Bieberbach’s theorems
• 9. Seifert manifolds with $\Gamma \setminus G/K$-fiber
• 10. Locally injective Seifert fiberings with torus fibers
• 11. Applications
• 12. Seifert fiberings with compact connected $Q$
• 13. Deformation spaces
• 14. $S^1$-actions on 3-dimensional manifolds
• 15. Classification of Seifert 3-manifolds via equivariant cohomology

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Volume: 1662010; 396 pp
MSC: Primary 55; 57; Secondary 53; 58;

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.

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

• Chapters
• 1. Transformation groups
• 2. Group actions and the fundamental group
• 3. Actions of compact Lie groups on manifolds
• 4. Definition of Seifert fibering
• 5. Group cohomology
• 6. Lie groups
• 7. Seifert fiber space construction for $G\times W$
• 8. Generalization of Bieberbach’s theorems
• 9. Seifert manifolds with $\Gamma \setminus G/K$-fiber
• 10. Locally injective Seifert fiberings with torus fibers
• 11. Applications
• 12. Seifert fiberings with compact connected $Q$
• 13. Deformation spaces
• 14. $S^1$-actions on 3-dimensional manifolds
• 15. Classification of Seifert 3-manifolds via equivariant cohomology
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