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Interpretation of quandle invariants in terms of knot group representations
by
Michael Eisermann
Institut Fourier, University of Grenoble
The classical knot group and the more recent invention of knot quandles are closely related concepts, and so it is not surprising to expect relationships between the various invariants derived from them. It is less obvious, however, to make the transition explicit and to establish a precise dictionary between both points of view. This endeavour is nevertheless important for the mutual benefit of the two approaches, and indispensable if we wish to exploit classical results in the quandle framework.
In this talk I will present some results that establish such an explicit correspondence. In particular my aim is to interpret the fundamental class in the second homology group of the knot quandle, and to represent quandle homology state-sum invariants by knot group representations.
Date received: November 10, 2006
Copyright © 2006 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # catp-07.