论文标题
简单复合物的最小体积熵
Minimal volume entropy of simplicial complexes
论文作者
论文摘要
本文介绍了拓扑假设，在这些假设下，封闭的歧管的最小体积熵，更普遍地是有限的简单复合物，消失或呈阳性。在本文的第一部分中，我们介绍了从给定有限的简单络合物到较低尺寸的简单复合物的基本纤维纤维纤维基本组的增长，以辅助拓扑条件，这确保了简单复合物的最小体积熵，既可以消失或阳性。我们还提供了有限的简单复合物的示例，其简单量为零，任意较大的体积熵。在本文的第二部分中，我们介绍了与有限的简单复合物基本组中某些亚组的指数增长以及其分类空间的拓扑拓扑相关的，其最小体积熵为正。整个文本中都列出了几个示例。
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present complementing topological conditions expressed in terms of the growth of the fundamental group of the fibers of maps from a given finite simplicial complex to simplicial complexes of lower dimension which ensure that the minimal volume entropy of the simplicial complex either vanishes or is positive. We also give examples of finite simplicial complexes with zero simplicial volume and arbitrarily large minimal volume entropy. In the second part of the article, we present topological assumptions related to the exponential growth of certain subgroups in the fundamental group of a finite simplicial complex and to the topology of the loop space of its classifying space under which the minimal volume entropy is positive. Several examples are presented throughout the text.
