Polynomial invariants of links satisfying cubic skein relations

2000/09/27 by Paolo Bellingeri, Bellingeri, Paolo, Louis Funar +1
Mathematics · #16S15 #57M27 #81R15 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:16S15 #msc:57M27 #msc:81R15

paper · pdf · doi:10.48550/arxiv.math/0009233

revised version, 28p, Asian J. Math., to appear

arxiv created 2004/02/27 · arxiv updated 2009/11/30

Abstract

The aim of this paper is to define two link invariants satisfying cubic skein relations. In the hierarchy of polynomial invariants determined by explicit skein relations they are the next level of complexity after Jones, HOMFLY, Kauffman and Kuperberg's G₂ quantum invariants. Our method consists in the study of Markov traces on a suitable tower of quotients of cubic Hecke algebras extending Jones approach.

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