Finite type invariants of nanowords and nanophrases
Geometric Topology
2010-10-05 v2
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.
Keywords
Cite
@article{arxiv.1007.1693,
title = {Finite type invariants of nanowords and nanophrases},
author = {Andrew Gibson and Noboru Ito},
journal= {arXiv preprint arXiv:1007.1693},
year = {2010}
}
Comments
29 pages. Second version: Corrected Proposition 5.14; added Remarks 8.4 and 8.5