Cubic Hecke Algebras and Invariants of Transversal Links
arXiv:1307.5862 · doi:10.1134/S1064562414010347
Abstract
We propose a purely algebraic approach to construct invariants of transversal links in the standard contact structure on the 3-sphere generalizing Jones' approach to invariant of usual links. The only geometry used is the analogue of Alexander and Markov theorems. More precisely, we construct a trace on a certain cubic Hecke algebra which is invariant under positive Markov moves only (we propose to call it a semi-Markov trace). The trace takes its values in the quotient of a polynomial ring by a certain ideal. An algorithm for computing a Groebner base of the ideal is given.
6 pages, 2 figures