Homotopy invariants of Gauss words

Details Homotopy invariants of Gauss words Homotopy invariants of Gauss words

2009-01-31

arxiv.org/abs/0902.0062v2

Mathematics

Geometric Topology

15 pages, 4 figures. Second version: added reference, corrected some comments

Scientific paper

By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.

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