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Finite type invariants of nanowords and nanophrases
- Publication Year :
- 2010
-
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.<br />Comment: 29 pages. Second version: Corrected Proposition 5.14; added Remarks 8.4 and 8.5
- Subjects :
- Mathematics - Geometric Topology
57M99 (Primary), 68R15 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1007.1693
- Document Type :
- Working Paper