Cubic Hecke Algebras and Invariants of Transversal Links
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arXiv
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| Format: | Preprint |
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2013
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| _version_ | 1866913595479031808 |
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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 |
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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 |