Orders of the canonical vector bundles over configuration spaces of finite graphs

Frederick R. Cohen and Ruizhi Huang

Vol. 316 (2022), No. 1, 53–64

DOI: 10.2140/pjm.2022.316.53

Abstract

We prove that the order of the canonical vector bundle over the configuration space is $2$ for a general planar graph, and is $4$ for a nonplanar graph.

To the memory of Professor Wen-Tsün Wu

Keywords

configuration space, vector bundle, finite graph

Mathematical Subject Classification

Primary: 55R10, 55R80

Secondary: 05C10, 55P15, 55P40

Milestones

Received: 31 January 2021

Revised: 17 July 2021

Accepted: 17 September 2021

Published: 26 February 2022