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Imbeddings of Three-Manifold Groups

Francisco González-AcuñaWilbur Carrington Whitten

出版	American Mathematical Soc., 1992
主題	Mathematics / Geometry / Differential
ISBN	08218253489780821825341
URL	http://books.google.com.hk/books?id=RHnUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.