Imbeddings of Three-Manifold Groups

Download or read book Imbeddings of Three-Manifold Groups written by Francisco González-Acuña and published by American Mathematical Soc.. This book was released on 1992 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the two broad questions of how 3-manifold groups imbed in one another and how such imbeddings relate to any corresponding [lowercase Greek]Pi1-injective maps. In particular, we are interested in 1) determining which 3-manifold groups are no cohopfian, that is, which 3-manifold groups imbed properly in themselves, 2) determining the knot subgroups of a knot group, and 3) determining when surgery on a knot [italic]K yields a lens (or "lens-like") space and the relationship of such a surgery to the knot-subgroup structure of [lowercase Greek]Pi1([italic]S3 - [italic]K). Our work requires the formulation of a deformation theorem for [lowercase Greek]Pi1-injective maps between certain kinds of Haken manifolds and the development of some algebraic tools.