Minimal volume entropy and fiber growth
Minimal volume entropy and fiber growth
复制标题
最小体积熵和纤维生长
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
S. Sabourau
中科院分区：
文献类型：
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作者：
I. Babenko;S. Sabourau
本文涉及的拓扑假设下，最小体积熵的封闭流形$M$，更一般的有限单纯复杂的$X$，消失或为正。这些拓扑条件表示为从给定的有限单纯复形$X$到低维单纯复形$P$的映射的纤维的基本群的增长。我们也给出了具有零单纯体积和任意大的最小体积熵的有限单纯复形的例子。
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold $M$, and more generally of a finite simplicial complex $X$, vanishes or is positive. These topological conditions are expressed in terms of the growth of the fundamental group of the fibers of maps from a given finite simplicial complex $X$ to lower dimensional simplicial complexes $P$. We also give examples of finite simplicial complexes with zero simplicial volume and arbitrarily large minimal volume entropy.