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On a conjecture of Louis H. Kauffman on alternative and pseudoalternating links
by
Marithania SilveroCasanova
Universidad de Sevilla, Spain and Indiana University
In 1983 Louis Kauffman introduced the family of alternative links, as a generalization of alternating links. It is known that alternative links are pseudoalternating. Kauffman conjectured the converse. In this talk we show that both families are equal in the particular case of knots of genus one. However, Kauffman's Conjecture does not hold in general, as we also show by finding two counterexamples. In the way we will deal with the intermediate family of homogeneous links, introduced by Peter Cromwell; the techniques used here allow us to give an explicit characterization of homogeneous links of genus 1. It was here, at GWU, 2 years ago when I presented the problem and my initial work on it.
Paper reference: arXiv:1402.4599
Date received: February 25, 2015
Copyright © 2015 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 # cbkp-15.