Magnitude homology in low degree
Magnitude homology in low degree
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低度幅度同源性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Kiyonori Gomi
中科院分区：
文献类型：
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作者：
Kiyonori Gomi
本文研究测地度量空间的第二、三、四模同调群：我们首先用某些单纯复形的第零同调群刻画一般度量空间的第二模同调群。然后，在测地度量空间上，我们用测地线来解释这一描述。测地度量空间的第三模同调也允许用单纯复形来刻画。在度量空间上的一个假设下，单纯的描述允许我们引入一个三阶同调类的不变量作为交数。最后，我们利用与测地线对相关的显式基来刻画具有一个假设的测地度量空间的第四模同调。
This paper studies the second, third and forth magnitude homology groups of geodesic metric spaces: We start with a description of the second magnitude homology of a general metric space in terms of the zeroth homology groups of certain simplicial complexes. Then, on a geodesic metric space, we interpret the description by means of geodesics. The third magnitude homology of a geodesic metric space also admits a description in terms of a simplicial complex. Under an assumption on a metric space, the simplicial description allows us to introduce an invariant of third magnitude homology classes as an intersection number. Finally, we describe the forth magnitude homology of a geodesic metric space with an assumption by using an explicit basis associated to pairs of geodesics.