On Generalization of Homotopy of Words and Its Applications

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 $S$-homotopy invariant of nanowords with some homotopy data $S$.

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

References in corpus (1)

• Homotopy classification of nanophrases with less than or equal to four letters