On a canonical lift of Artin's representation to loop braid groups

[摘要] Each pointed topological space has an associated pi-module, obtained from action of its first homotopy group on its second homotopy group. For the 3-ball with a trivial link with n-components removed from its interior, its pi-module Mn is of free type. In this paper we give an injection of the (extended) loop braid group into the group of automorphisms of Mn. We give a topological interpretation of this injection, showing that it is both an extension of Artin's representation for braid groups and of Dahm's homomorphism for (extended) loop braid groups. (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01