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Magnitude homology and homotopy type of metric fibrations

Authors :
Asao, Yasuhiko
Tajima, Yu
Yoshinaga, Masahiko
Publication Year :
2024

Abstract

In this article, we show that each two metric fibrations with a common base and a common fiber have isomorphic magnitude homology, and even more, the same magnitude homotopy type. That can be considered as a generalization of a fact proved by T. Leinster that the magnitude of a metric fibration with finitely many points is a product of those of the base and the fiber. We also show that the definition of the magnitude homotopy type due to the second and the third authors is equivalent to the geometric realization of Hepworth and Willerton's pointed simplicial set.<br />Comment: 12 pages

Subjects

Subjects :
Mathematics - Algebraic Topology

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2409.03278
Document Type :
Working Paper