Damiani, C, Goncalves Faria Martins, J orcid.org/0000-0001-8113-3646 and Martin, PP (2021) On a canonical lift of Artin's representation to loop braid groups. Journal of Pure and Applied Algebra, 225 (12). 106760. ISSN 0022-4049
Abstract
Each pointed topological space has an associated π-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 π-module is of free type. In this paper we give an injection of the (extended) loop braid group into the group of automorphisms of . 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.
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Copyright, Publisher and Additional Information: | © 2021 Elsevier B.V. All rights reserved. This is an author produced version of an article published in Journal of Pure and Applied Algebra. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | Primary; 20F36; secondary; 57Q45 | ||||
Dates: |
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 23 Apr 2021 13:15 | ||||
Last Modified: | 20 Apr 2022 00:38 | ||||
Status: | Published | ||||
Publisher: | Elsevier | ||||
Identification Number: | https://doi.org/10.1016/j.jpaa.2021.106760 |