Cubical setting for discrete homotopy theory, revisited

被引：0

作者：

Carranza, D. ^{[1
]}

Kapulkin, K. ^{[2
]}

机构：

[1] Johns Hopkins Univ, Dept Math, Krieger Hall 211,3400 N Charles St, Baltimore, MD 21218 USA

[2] Univ Western Ontario, Dept Math, Middlesex Coll 255C,1151 Richmond St, London, ON N6A 5B7, Canada

来源：

COMPOSITIO MATHEMATICA | 2025年 / 160卷 / 12期

基金：

加拿大自然科学与工程研究理事会;

关键词：

discrete homotopy theory; cubical set; reflexive graph; Kan complex; PATTERNS; ALGEBRA;

D O I：

10.1112/S0010437X24007486

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use this to prove a conjecture of Babson, Barcelo, de Longueville, and Laubenbacher from 2006, and a strong version of the Hurewicz theorem in discrete homotopy theory.

引用

页数：49

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