The space of Heegaard splittings
The space of Heegaard splittings
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Heegaard 分裂空间
DOI：
10.1515/crelle.2012.016
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Darryl McCullough
中科院分区：
文献类型：
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作者：
Jesse Johnson;Darryl McCullough
对于可定向闭三维流形M中的Heegaard曲面，我们用φ（M，φ）= Diff（M）/Diff（M，φ）表示与Heegaard分裂（M，φ）等价的Heegaard曲面空间。它的路径分量是Heegaard分裂等价于（M，M）的合痕类。我们用Diff（M）和（M，n）的Goeritz群来描述H（M，n）.特别地，对于双曲M，每个路径分量都是Goeritz群的分类空间，并且当（M，<$）的（Hempel）距离大于3时，<$（M，<$）的每个路径分量都是可收缩的。对于亏格为0或1的分裂，我们确定了完全同伦类型（在M未知的情况下模M的Smale猜想）。
Abstract For a Heegaard surface Σ in a closed orientable 3-manifold M, we denote by ℋ(M, Σ) = Diff(M)/Diff(M, Σ) the space of Heegaard surfaces equivalent to the Heegaard splitting (M, Σ). Its path components are the isotopy classes of Heegaard splittings equivalent to (M, Σ). We describe H(M, Σ) in terms of Diff(M) and the Goeritz group of (M, Σ). In particular, for hyperbolic M each path component is a classifying space for the Goeritz group, and when the (Hempel) distance of (M, Σ) is greater than 3, each path component of ℋ(M, Σ) is contractible. For splittings of genus 0 or 1, we determine the complete homotopy type (modulo the Smale Conjecture for M in the cases when it is not known).