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On higher order link polynomials
by
Yongwu Rong
George Washington University
Higher order link polynomials were defined by combining ingredients from link polynomials and Vassiliev invariants. In this talk, we will survey the following results on this topic:
1. The classification of the order 1 Homfly polynomial, done by the speaker.
2. The theorem that each nth partial derivatives of the Homfly polynomials is a higher order Homfly polynomial of order n, due to Lickorish and the speaker. This also greatly simplifies the work in (1).
3. The determination of the free part of the higher order Conway skein module, due to Andersen and Turaev.
4. An affirmative answer to the question, asked by Lickorish-Rong, whether all partial derivatives of the Homfly link polynomials are linearly independent.
5. The classification of all the higher order Conway polynomials, following work of the above.
Date received: January 24, 2000
Copyright © 2000 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 # caea-18.