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Homotopy Equivalences Of 3-manifolds And Deformation Theory Of Kleinian Groups (memoirs Of The American Mathematical Society) by Richard Douglas Canary; Darryl McCullough is a nonfiction available to read on EtoBox.

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<p>This text investigates a natural question arising in the topological theory of $3$-manifolds, and applies the results to give new information about the deformation theory of hyperbolic $3$-manifolds. It is well known that some compact $3$-manifolds with boundary admit homotopy equivalences that are not homotopic to homeomorphisms. We investigate when the subgroup $\mathcal{R}(M)$ of outer automorphisms of $\pi_1(M)$ which are induced by homeomorphisms of a compact $3$-manifold $M$ has finite index in the group $\operatorname{Out}(\pi_1(M))$ of all outer automorphisms. This question is completely resolved for Haken $3$-manifolds. It is also resolved for many classes of reducible $3$-manifolds and $3$-manifolds with boundary patterns, including all pared $3$-manifolds. The components of the interior $\operatorname{GF}(\pi_1(M))$ of the space $\operatorname{AH}(\pi_1(M))$ of all (marked) hyperbolic $3$-manifolds homotopy equivalent to $M$ are enumerated by the marked homeomorphism types of manifolds homotopy equivalent to $M$, so one may apply the topological results above to study the topology of this deformation space. We show that $\operatorname{GF}(\pi_1(M))$ has finitely many

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Author

Richard Douglas Canary; Darryl McCullough

Publisher

American Mathematical Society

Published

2004

Language

EN

ISBN

9780821835494

Category

nonfiction

Subjects

Mathematics, Science, Stem