Mapping fiber, loop and suspension graphs in naive discrete homotopy theory

2024/02/24 by So Yamagata, Yamagata, So
Computer Science · Mathematics · #05C25 #55P10 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2402.15714

openalex publication_date 2024/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the (non-)similarities between the A-homotopy and ordinary homotopy theories through explicit constructions. More precisely, we define mapping fiber graphs and study their basic properties yielding, under a technical condition, a discrete analogous of Puppe sequence in a naive discrete homotopy theory.

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