Imbeddings Of Three-Manifold Groups

Deals with the two broad questions of how three-manifold groups imbed in one another and how such imbeddings relate to any corresponding pi-one-injective maps. In particular, the authors are concerned with determining which three-manifold groups imbed properly in themselves, finding the knot subgroups of a knot group, and investigating when surgery

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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 *p-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 *p[1(S - *K). The authors use the formulation of a deformation theorem for *p[1-injective maps between certain kinds of Haken manifolds and develop some algebraic tools.