Finite type invariants of nanowords and nanophrases |
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Authors: | Andrew Gibson Noboru Ito |
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Affiliation: | a Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan b Department of Mathematics, Waseda University, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan |
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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 1 and degree 2 respectively. We also give a finite type invariant of degree 4 for open homotopy of Gauss words. |
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Keywords: | primary, 57M99 secondary, 68R15 |
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