Lectures on topology of words
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- Turaev, V. Jpn. J. Math. (2007) 2: 1. doi:10.1007/s11537-007-0634-2
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We discuss a topological approach to words introduced by the author in [Tu2]–[Tu4]. Words on an arbitrary alphabet are approximated by Gauss words and then studied up to natural modifications inspired by the Reidemeister moves on knot diagrams. This leads us to a notion of homotopy for words. We introduce several homotopy invariants of words and give a homotopy classification of words of length five.