Finite type invariants of nanowords and nanophrases

Andrew Gibson*, Noboru Ito

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1050-1072
Number of pages23
JournalTopology and its Applications
Issue number8
Publication statusPublished - 2011 May 15


  • Finite type invariant
  • Homotopy invariant
  • Nanophrases
  • Nanowords
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Geometry and Topology


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