Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Seifert Fiberings
 
Kyung Bai Lee University of Oklahoma, Norman, OK
Frank Raymond University of Michigan, Ann Arbor, MI
Front Cover for Seifert Fiberings
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
Front Cover for Seifert Fiberings
Click above image for expanded view
  • Front Cover for Seifert Fiberings
  • Back Cover for Seifert Fiberings
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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Request Review Copy
  • Get Permissions
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.

Readership

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
You may be interested in...
Please select which format for which you are requesting permissions.