The homology digraph of a preordered space

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2024-07-27 DOI:10.1007/s40062-024-00352-7

Catarina Faustino, Thomas Kahl

引用次数: 0

Abstract

This paper studies a notion of directed homology for preordered spaces, called the homology digraph. We show that the homology digraph is a directed homotopy invariant and establish variants of the main results of ordinary singular homology theory for the homology digraph. In particular, we prove a Künneth formula, which enables one to compute the homology digraph of a product of preordered spaces from the homology digraphs of the components.

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有序空间的同源数图

本文研究有序空间的有向同调概念，即同调数字图。我们证明了同调数字图是有向同调不变式，并为同调数字图建立了普通奇异同调理论主要结果的变体。特别是，我们证明了一个库奈特公式，通过这个公式，我们可以从各部分的同调数字图计算出预序空间乘积的同调数字图。

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

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.