Simplified numerical form of universal finite type invariant of Gauss words
| Autor: | Fukunaga, Tomonori, Yamaguchi, Takayuki, Yamanoi, Takaaki |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0218216513500375 |
| Popis: | In the present paper, we study the finite type invariants of Gauss words. In the Polyak algebra techniques, we reduce the determination of the group structure to transformation of a matrix into its Smith normal form and we give the simplified form of a universal finite type invariant by means of the isomorphism of this transformation. The advantage of this process is that we can implement it as a computer program. We obtain the universal finite type invariant of degree 4, 5, and 6 explicitly. Moreover, as an application, we give the complete classification of Gauss words of rank 4 and the partial classification of Gauss words of rank 5 where the distinction of only one pair remains. Comment: 12 pages, 3 tables |
| Databáze: | arXiv |
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