English

On Generalization of Homotopy of Words and Its Applications

Geometric Topology 2009-10-29 v2 Combinatorics

Abstract

V. Turaev introduced the theory of topology of words and phrases in 2005. This is a combinatorialy extension of the theory of virtual knots and links. In this paper we generalize the notion of homotopy of words and phrases and we give geometric meanings of the generalized homotopy of words. Moreover using the generalized homotopy theory of words and phrases, we extend some homotopy invariants of nanophrases to SS-homotopy invariant of nanowords with some homotopy data SS.

Keywords

Cite

@article{arxiv.0908.2899,
  title  = {On Generalization of Homotopy of Words and Its Applications},
  author = {Tomonori Fukunaga},
  journal= {arXiv preprint arXiv:0908.2899},
  year   = {2009}
}

Comments

21 pages, 1 figure; We modified the definition of some invariants. See Remark 5.3