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Homeomorphisms of $3$-Manifolds with Compressible Boundary
Darryl McCulloughAndy Miller
出版American Mathematical Soc., 1986
主題Mathematics / Differential Equations / GeneralMathematics / Geometry / GeneralMathematics / Geometry / DifferentialMathematics / Topology
ISBN08218234699780821823460
URLhttp://books.google.com.hk/books?id=kz3UCQAAQBAJ&hl=&source=gbs_api
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註釋The authors study the mapping class groups of orientable [italic]P2-irreducible 3-manifolds with compressible boundary, and extend the results proved by K. Johannson for the boundary incompressible case. The authors show that the mapping class group is finitely-generated and has a geometrically defined subgroup of finite index. The main tool used in the proof of the results is to reduce the theorems to analogous statements about incompressible neighborhoods of compressible boundary components, and, using the fact that they have a very simple structure (being products-with-handles), to apply geometric techniques. Appropriate extensions of the results of the nonorientable [italic]P2-irreducible 3-manifolds are also given.