Cubic Hecke Algebras and Invariants of Transversal Links

Fuente: arXiv
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Main Author: Orevkov, S. Yu.
Format: Preprint
Published: 2013
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author Orevkov, S. Yu.
author_facet Orevkov, S. Yu.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_1307_5862
institution arXiv
publishDate 2013
record_format arxiv
spellingShingle Cubic Hecke Algebras and Invariants of Transversal Links
Orevkov, S. Yu.
Geometric Topology
57M27
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.
title Cubic Hecke Algebras and Invariants of Transversal Links
topic Geometric Topology
57M27
url https://arxiv.org/abs/1307.5862