Name Tomonori Fukunaga Hokkaido University Session Jan 11 16:20~16:40 E11-102 On braid type theory of nanophrases In this talk we define braid type phrases'' which is a generalization of the notion of virtual braids. Then we talk about relation between braid type phrase and the homotopy theory of nanophrases. More precisely we introduce Alexander type theorem and Markov type theorem for braid type phrases. We also talk on a group structure of braid type phrases and some representations of braid type phrase groups if possible. 102-1-11/20121011KAIST.pdf