Mathematische Annalen

, Volume 349, Issue 4, pp 871–887

Homotopy invariants of Gauss words

Article

Abstract

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 homotopic 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.

Mathematics Subject Classification (2000)

Primary 57M99 Secondary 68R15 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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