Cubic Hecke Algebras and Invariants of Transversal Links

S. Yu. Orevkov

doi:10.1134/s1064562414010347

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arXiv · 1307.5862

Cubic Hecke Algebras and Invariants of Transversal Links

S. Yu. Orevkov

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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.

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BibTeX RIS

S. Yu. Orevkov. 2013-07-22. Cubic Hecke Algebras and Invariants of Transversal Links. https://doi.org/10.1134/s1064562414010347

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