Martins, JF and Picken, R (2015) Link invariants from finite categorical groups. Homology, Homotopy and Applications, 17 (2). pp. 205-233. ISSN 1532-0073
Abstract
We define an invariant of tangles and framed tangles, given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks, quandles, rack and quandle cocycles, and central extensions of groups. We prove that our construction includes all rack and quandle cohomology (framed) link invariants, as well as the Eisermann invariant of knots. We construct a class of Reidemeister pairs which constitute a lifting of the Eisermann invariant, and show through an example that this class is strictly stronger than the Eisermann invariant itself.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of a paper published in Homology, Homotopy and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | knot invariant, tangle, peripheral system, quandle, rack, crossed module, categorical group, non-abelian tensor product of groups |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Apr 2017 12:14 |
Last Modified: | 25 Jun 2018 10:34 |
Published Version: | https://doi.org/10.4310/HHA.2015.v17.n2.a11 |
Status: | Published |
Publisher: | International Press |
Identification Number: | 10.4310/HHA.2015.v17.n2.a11 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112769 |