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
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Imbeddings of Three-Manifold Groups
 
Imbeddings of Three-Manifold Groups
eBook ISBN:  978-1-4704-0900-5
Product Code:  MEMO/99/474.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $16.80
Imbeddings of Three-Manifold Groups
Click above image for expanded view
Imbeddings of Three-Manifold Groups
eBook ISBN:  978-1-4704-0900-5
Product Code:  MEMO/99/474.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $16.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 991992; 55 pp
    MSC: Primary 55; 57;

    This work deals with the two broad questions of how three-manifold groups imbed in one another and how such imbeddings relate to any corresponding \(\pi _1\)-injective maps. The focus is on when a given three-manifold covers another given manifold. In particular, the authors are concerned with 1) determining which three-manifold groups are not cohopfian—that is, which three-manifold groups imbed properly in themselves; 2) finding the knot subgroups of a knot group; and 3) investigating when surgery on a knot \(K\) yields lens (or “lens-like”) spaces and how this relates to the knot subgroup structure of \(\pi _1(S^3-K)\). The authors use the formulation of a deformation theorem for \(\pi _1\)-injective maps between certain kinds of Haken manifolds and develop some algebraic tools.

    Readership

    Researchers in lower-dimensional topology (knot theory and three-dimensional manifolds).

  • Table of Contents
     
     
    • Chapters
    • 1. Deformation theorems
    • 2. Cohopficity
    • 3. Coverings between knot exteriors
    • 4. Subgroups of finite index
    • 5. Knot subgroups of torus-knot groups
    • 6. Depth, and loose and tight subgroups
    • 7. Knot subgroups of knot groups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 991992; 55 pp
MSC: Primary 55; 57;

This work deals with the two broad questions of how three-manifold groups imbed in one another and how such imbeddings relate to any corresponding \(\pi _1\)-injective maps. The focus is on when a given three-manifold covers another given manifold. In particular, the authors are concerned with 1) determining which three-manifold groups are not cohopfian—that is, which three-manifold groups imbed properly in themselves; 2) finding the knot subgroups of a knot group; and 3) investigating when surgery on a knot \(K\) yields lens (or “lens-like”) spaces and how this relates to the knot subgroup structure of \(\pi _1(S^3-K)\). The authors use the formulation of a deformation theorem for \(\pi _1\)-injective maps between certain kinds of Haken manifolds and develop some algebraic tools.

Readership

Researchers in lower-dimensional topology (knot theory and three-dimensional manifolds).

  • Chapters
  • 1. Deformation theorems
  • 2. Cohopficity
  • 3. Coverings between knot exteriors
  • 4. Subgroups of finite index
  • 5. Knot subgroups of torus-knot groups
  • 6. Depth, and loose and tight subgroups
  • 7. Knot subgroups of knot groups
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.