Lectures on Topology of Words

Details Lectures on Topology of Words Lectures on Topology of Words

2006-09-19

arxiv.org/abs/math/0609516v1

Mathematics

Combinatorics

40 pages, lecture notes for a series of lectures given in RIMS, Kyoto University in February 2006

Scientific paper

We discuss a topological approach to words introduced by the author. 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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