Memoirs of the American Mathematical Society 1992; 55 pp; softcover Volume: 99 ISBN10: 0821825348 ISBN13: 9780821825341 List Price: US$28 Individual Members: US$16.80 Institutional Members: US$22.40 Order Code: MEMO/99/474
 This work deals with the two broad questions of how threemanifold groups imbed in one another and how such imbeddings relate to any corresponding \(\pi _1\)injective maps. The focus is on when a given threemanifold covers another given manifold. In particular, the authors are concerned with 1) determining which threemanifold groups are not cohopfianthat is, which threemanifold 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 "lenslike") spaces and how this relates to the knot subgroup structure of \(\pi _1(S^3K)\). 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 lowerdimensional topology (knot theory and threedimensional manifolds). Table of Contents  Deformation theorems
 Cohopficity
 Coverings between knot exteriors
 Subgroups of finite index
 Knot subgroups of torusknot groups
 Depth, and loose and tight subgroups
 Knot subgroups of knot groups
