Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 1–39

Lectures on topology of words

original article

DOI: 10.1007/s11537-007-0634-2

Cite this article as:
Turaev, V. Jpn. J. Math. (2007) 2: 1. doi:10.1007/s11537-007-0634-2


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.

Keywords and phrases:

words curves homotopy 

Mathematics Subject Classification (2000):

57M99 68R15 

Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.IRMAUniversité Louis Pasteur - C.N.R.S.StrasbourgFrance

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