2008/06/30 by Jason Callahan, JASON CALLAHAN
Mathematics · #Algebraic Geometry and Number Theory #Conjecture #Conjugate #Geometric and Algebraic Topology #Knot (papermaking) #Knot theory #Link (geometry) #Mathematics and Applications #Skein relation #Trefoil knot #Tricolorability #math.GT #msc:57M05 #msc:57M25
paper · pdf · doi:10.1142/s0218216510008248
published in Journal of Knot Theory and Its Ramifications 19(07), 905-916 (World Scientific) · 10 pages, submitted to Journal of Knot Theory and Its Ramifications
arxiv created 2009/01/16 · openalex publication_date 2010/07/01 · arxiv updated 2013/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This note establishes a stronger version of a conjecture of Reid and others in the arithmetic case: if two elements of equal trace (e.g. conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic (and hence peripheral). This includes the figure-eight knot and Whitehead link groups. Similarly, if two conjugate elements generate the trefoil knot group, then the elements are peripheral.