The fiber of persistent homology for trees.

David Beers, Jacob Leygonie
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Abstract

Consider the space of continuous functions on a geometric tree X whose persistent homology gives rise to a finite generic barcode D. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is D. We find that each component is homotopy equivalent to a configuration space on X with specialised constraints encoded by the merge tree. For barcodes D with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.

Abstract Image

Abstract Image

Abstract Image

树木持久同源性的纤维。
考虑几何树X上的连续函数空间,其持久的同构性产生了有限的一般条形码d。我们证明了在这个空间中有与条形码为d的合并树一样多的路径连接分量。我们发现每个分量都等价于X上具有由合并树编码的特殊约束的位形空间。对于具有一个或两个间隔的条形码D,我们的方法也允许我们计算这个函数空间的同伦类型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.40
自引率
0.00%
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0
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