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Lectures on topology of words

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Abstract.

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.

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Authors and Affiliations

  1. IRMA, Université Louis Pasteur - C.N.R.S., 7 rue René Descartes, F-67084, Strasbourg, France

    Vladimir Turaev

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  1. Vladimir Turaev
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Correspondence to Vladimir Turaev.

Additional information

Communicated by: Toshiyuki Kobayashi

Based on notes by Eri Hatakenaka, Daniel Moskovich, and Tadayuki Watanabe

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Turaev, V. Lectures on topology of words. Jpn. J. Math. 2, 1–39 (2007). https://doi.org/10.1007/s11537-007-0634-2

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  • DOI: https://doi.org/10.1007/s11537-007-0634-2

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