Mathematische Annalen

, Volume 349, Issue 4, pp 871–887

Homotopy invariants of Gauss words


DOI: 10.1007/s00208-010-0536-0

Cite this article as:
Gibson, A. Math. Ann. (2011) 349: 871. doi:10.1007/s00208-010-0536-0


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 57M99Secondary 68R15

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan