Homotopy groups of cubical sets

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-10-07 DOI:10.1016/j.exmath.2023.125518

Daniel Carranza , Krzysztof Kapulkin

引用次数: 0

Abstract

We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric realization functor. We also provide purely combinatorial proofs of several classical theorems, including: product preservation, commutativity of higher homotopy groups, the long exact sequence of a fibration, and Whitehead’s theorem.

This is a companion paper to our “Cubical setting for discrete homotopy theory, revisited” in which we apply these results to study the homotopy theory of simple graphs.

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三次集的同伦群

定义并研究了三次集的同伦群。为此，我们给出了三次集合的同伦群的四种定义，通过几何实现函子证明了它们是等价的，并进一步证明了它们与它们的拓扑类似物一致。我们还提供了几个经典定理的纯组合证明，包括:乘积保存、高同伦群的交换性、纤支的长精确序列和Whitehead定理。这是我们的“离散同伦理论的三次设置，重访”的配套论文，我们应用这些结果来研究简单图的同伦理论。

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

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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