2019-10-15T18:40:26Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697282018-04-25T23:44:10Zhdl_2115_45007hdl_2115_116HOMOTOPY CLASSIFICATION OF NANOPHRASES WITH LESS THAN OR EQUAL TO FOUR LETTERSFukunaga, TomonoriNanophrasesHomotopyMulti-component curvesStably equivalent410In this paper we give the classification of stable equivalence classes of ordered, pointed, riented multi-component curves on surfaces with minimum crossing number less than r equal to 2 which any curve in its equivalent class has no simply closed curves in its omponents. To do this, we use the theory of words and phrases which was introduced y V. Turaev. Indeed we give the homotopy classification of nanophrases with less than r equal 4 letters. This is an extension of the classification of nanophrases of length 2 ith less than or equal to 4 letters which was given by the author in the recent paper.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69728info:doi/10.14943/84070https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69728/1/pre921.pdfHokkaido University Preprint Series in Mathematics9211112008engpublisher