Homeomorphisms of $3$-Manifolds with Compressible Boundary
Darryl McCullough · Andy Miller
Jan 1986 · American Mathematical Society: Memoirs of the American Mathematical Society Book 344 · American Mathematical Soc.
Ebook
100
Pages
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About this ebook
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.
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