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arXiv · 1209.0287

Simplified numerical form of universal finite type invariant of Gauss words

Tomonori Fukunaga·Takayuki Yamaguchi·Takaaki Yamanoi
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Abstract

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.

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Tomonori Fukunaga, Takayuki Yamaguchi, Takaaki Yamanoi. 2012-09-03. Simplified numerical form of universal finite type invariant of Gauss words. https://doi.org/10.1142/s0218216513500375

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