2024-03-29T10:20:58Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697482022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116HOMOTOPY CLASSIFICATION OF GENERALIZED PHRASES IN TURAEV'S THEORY OF WORDSFukunaga, Tomonoriwordsphraseshomotopy of words and phrases410In 2005 V. Turaev introduced the theory of topology of words and hrases. Turaev defined an equivalence relation on generalized words and phrases hich is called homotopy. This is suggested by the Reidemeister moves in the not theory. Then Turaev gave the homotopy classification of generalized words ith less than or equal to five letters. In this paper we give the classification of eneralized phrases up to homotopy with less than or equal to three letters. To o this we construct a new homotopy invariant for nanophrases over any α.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69748info:doi/10.14943/84088https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69748/1/pre940.pdfHokkaido University Preprint Series in Mathematics9401122009-05-01engpublisher