Link homotopy invariant quandles
Journal of Knot Theory and its Ramifications
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.
Hughes, James R., "Link homotopy invariant quandles" (2011). Faculty Publications. 1282.