Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
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3-流形相对微分同胚群分类空间的有限性
DOI：
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发表时间：
1997
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通讯作者：
Darryl McCullough
中科院分区：
文献类型：
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作者：
A. Hatcher;Darryl McCullough
主要定理表明，如果M是一个具有非空边界的不可约紧连通3{流形，则限定在@M上的恒等映射的M的对纯空间的分类空间BDi （M rel @M）具有非球面CW{复的同伦类型。这回答了，对于这类流形，M Kontsevich提出的一个问题。主要定理来源于一个更精确的结果，即对于这些流形，映射类群H（M rel @M）被建立为紧连通曲面的相对映射类群中的自由阿贝尔群和nite索引子群的扩展序列。
The main theorem shows that if M is an irreducible compact connected ori- entable 3{manifold with non-empty boundary, then the classifying space BDi (M rel @M) of the space of dieomorphisms of M which restrict to the identity map on @M has the homotopy type of a nite aspherical CW{complex. This answers, for this class of manifolds, a question posed by M Kontsevich. The main theorem follows from a more precise result, which asserts that for these manifolds the mapping class group H(M rel @M) is built up as a se- quence of extensions of free abelian groups and subgroups of nite index in relative mapping class groups of compact connected surfaces.