2009/01/31 by Andrew Gibson, Gibson, Andrew
Mathematics · #57M99 (Primary) #68R15 (Secondary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M99 #msc:68R15
paper · pdf · doi:10.48550/arxiv.0902.0062
15 pages, 4 figures. Second version: added reference, corrected some comments
openalex publication_date 2009/01/31 · arxiv created 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.