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Homotopy Classification of Generalized Phrases in Turaev's Theory of Words

2009/04/27 by Tomonori Fukunaga, Fukunaga, Tomonori
Computer Science · Mathematics · #57M99 #68R15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:57M99 #msc:68R15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0904.4206

12 pages

arxiv created 2009/04/27 · openalex publication_date 2009/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In 2005 V. Turaev introduced the theory of topology of words and phrases. Turaev defined an equivalence relation on generalized words and phrases which is called homotopy. This is suggested by the Reidemeister moves in the knot theory. Then Turaev gave the homotopy classification of generalized words with less than or equal to five letters. In this paper we give the classification of generalized phrases up to homotopy with less than or equal to three letters. To do this we construct a new homotopy invariant for nanophrases over any α.

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