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Imbeddings of Three-Manifold Groups
F. González-Acuña and Wilbur C. Whitten

Memoirs of the American Mathematical Society
1992; 55 pp; softcover
Volume: 99
ISBN-10: 0-8218-2534-8
ISBN-13: 978-0-8218-2534-1
List Price: US$28
Individual Members: US$16.80
Institutional Members: US$22.40
Order Code: MEMO/99/474
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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.


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

Table of Contents

  • Deformation theorems
  • Cohopficity
  • Coverings between knot exteriors
  • Subgroups of finite index
  • Knot subgroups of torus-knot groups
  • Depth, and loose and tight subgroups
  • Knot subgroups of knot groups
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