Finite type invariants of nanowords and nanophrases

Details Finite type invariants of nanowords and nanophrases Finite type invariants of nanowords and nanophrases

2010-07-10

arxiv.org/abs/1007.1693v2

Mathematics

Geometric Topology

29 pages. Second version: Corrected Proposition 5.14; added Remarks 8.4 and 8.5

Scientific paper

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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