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.
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页数：49
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