**Memoirs of the American Mathematical Society**

1992;
55 pp;
Softcover

MSC: Primary 55; 57;

Print ISBN: 978-0-8218-2534-1

Product Code: MEMO/99/474

List Price: $28.00

Individual Member Price: $16.80

**Electronic ISBN: 978-1-4704-0900-5
Product Code: MEMO/99/474.E**

List Price: $28.00

Individual Member Price: $16.80

# Imbeddings of Three-Manifold Groups

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*F. González-Acuña; Wilbur Whitten*

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

# Table of Contents

## Imbeddings of Three-Manifold Groups

- Contents v6 free
- Abstract vi7 free
- Introduction vii8 free
- Chapter 1. Deformation Theorems 110 free
- Chapter 2. Cohopficity 615
- Chapter 3. Coverings Between Knot Exteriors 1019
- Chapter 4. Subgroups of Finite Index 1625
- Chapter 5. Knot Subgroups of Torus-Knot Groups 2938
- Chapter 6. Depth, and Loose and Tight Subgroups 3241
- Chapter 7. Knot Subgroups of Knot Groups 3746
- References 5261