Title

Link homotopy invariant quandles

Document Type

Article

Publication Title

Journal of Knot Theory and its Ramifications

Publication Date

5-1-2011

Abstract

We consider several approaches to defining a link homotopy version of the fundamental quandle Q(L) of a link L in S3. We first define the reduced fundamental quandle RQ(L) as a quotient of Q(L). We show that RQ(L) is a link homotopy invariant that carries at least as much information as the meridian-preserving isomorphism class of Milnor's reduced group RG(L). We then show that operator reduction, a plausible alternative approach to defining RQ(L), fails to yield a link homotopy invariant. Finally, we give a geometric characterization of RQ(L), and offer a caveat regarding a seemingly simpler approach. © 2011 World Scientific Publishing Company.

Volume

20

Issue

5

First Page

763

Last Page

773

DOI

10.1142/S0218216511008930

ISSN

02182165

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