Discrete homotopy and homology theories for finite posets

2024/10/22 by Jing-Wen Gao, Gao, Jing-Wen, Xiao‐Song Yang +1
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2410.16948

Abstract

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is related to the discrete homotopy theory through a discrete analogue of the Hurewicz map.

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