Finite type invariants of nanowords and nanophrases

Andrew Gibson; Noboru Ito

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arXiv · 1007.1693

Finite type invariants of nanowords and nanophrases

Andrew Gibson·Noboru Ito

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Abstract

Homotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual knots and links via semi-virtual crossings. We extend their definition to nanowords and nanophrases. We study finite type invariants of low degrees. In particular, we show that the linking matrix and T invariant defined by Fukunaga are finite type of degree one and degree two respectively. We also give a finite type invariant of degree 4 for open homotopy of Gauss words.

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Andrew Gibson, Noboru Ito. 2010-10-04. Finite type invariants of nanowords and nanophrases. https://arxiv.org/abs/1007.1693

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