Uniform Uniform Exponential Growth of Subgroups of the Mapping Class Group
Uniform Uniform Exponential Growth of Subgroups of the Mapping Class Group
复制标题
映射类组的子组的均匀均匀指数增长
DOI：
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发表时间：
2008
期刊：
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通讯作者：
J. Mangahas
中科院分区：
文献类型：
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作者：
J. Mangahas
设Mod（S）表示紧致可定向曲面S的映射类群.我们证明了Mod（S）的非虚交换的子群具有一致的指数增长，其最小增长率由一个仅依赖于且必然依赖于S的常数所限制。为了证明，我们发现在任何这样的子群明确的自由群生成元是“短”在任何字度量。除了边界增长之外，这还允许简单随机游走的返回概率有一个边界。
Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a constant depending only, and necessarily, on S. For the proof, we find in any such subgroup explicit free group generators which are “short” in any word metric. Besides bounding growth, this allows a bound on the return probability of simple random walks.