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

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

2009-04-27

arxiv.org/abs/0904.4206v1

Mathematics

Combinatorics

12 pages

Scientific paper

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 $\alpha$.

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