Mapping fiber, loop and suspension graphs in naive discrete homotopy theory
Combinatorics
2025-03-19 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.2402.15714,
title = {Mapping fiber, loop and suspension graphs in naive discrete homotopy theory},
author = {So Yamagata},
journal= {arXiv preprint arXiv:2402.15714},
year = {2025}
}
Comments
14 pages, 5 figures. Typographical errors explanations were corrected throughout. Any comments are welcomed