具有不可缩原象的持久同调

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-05-17 DOI:10.4310/hha.2022.v24.n2.a16

K. Mischaikow, C. Weibel

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引用次数: 4

摘要

.对于一个固定的N，我们分析了所有序列z=（z1，…，zN）的空间，用给定的持久图P逼近圆上的连续函数，并证明了该空间的典型分量与S1是同构等价的。我们还考虑了具有2点持久图的Y形（分别为星形）树上的函数空间，并证明了该空间与S1（分别为一束圆）是同构等价的。

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Persistent homology with non-contractible preimages

. For a ﬁxed N , we analyze the space of all sequences z = ( z 1 , . . . , z N ), approximating a continuous function on the circle, with a given persistence diagram P , and show that the typical components of this space are homotopy equivalent to S 1 . We also consider the space of functions on Y -shaped (resp., star-shaped) trees with a 2-point persistence diagram, and show that this space is homotopy equivalent to S 1 (resp., to a bouquet of circles).

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.