2009/08/20 by Tomonori Fukunaga, Fukunaga, Tomonori
Mathematics · #57M99 #68R15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GT #msc:57M99 #msc:68R15
paper · pdf · doi:10.48550/arxiv.0908.2899
21 pages, 1 figure; We modified the definition of some invariants. See Remark 5.3
openalex publication_date 2009/08/20 · arxiv created 2009/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.