Bounding the stable genera of Heegaard splittings from below
Bounding the stable genera of Heegaard splittings from below
复制标题
从下面界定 Heegaard 分裂的稳定属
DOI：
10.1112/jtopol/jtq021
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发表时间：
2008
影响因子：
1.1
通讯作者：
Jesse Johnson
中科院分区：
文献类型：
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作者：
Jesse Johnson
对于每个正整数k，我们刻画了一个具有亏格2k和2k−1的Heegaard曲面的3-流形，使得这两个曲面的任何公共稳定化都至少有亏格3k−1.我们还发现，对于每个k，都有一个具有边界的3-流形允许k和k+1亏格的Heegaard分裂，其稳定亏格为2k，并且对于每个正n，有n个相同亏格的两两非同位素Heegaard分裂的3-流形都是稳定的.
We describe for each positive integer k a 3‐manifold with Heegaard surfaces of genus 2k and 2k−1 such that any common stabilization of these two surfaces has genus at least 3k−1. We also find, for every k, a 3‐manifold with boundary admitting Heegaard splittings of genus k and k+1 whose stable genus is 2k, and for every positive n, a 3‐manifold that has n pairwise nonisotopic Heegaard splittings of the same genus all of which are stabilized.