Communications in Analysis and Geometry

Volume 18 (2010)

Number 1

Simon’s conjecture for two-bridge knots

Pages: 121 – 143

DOI: http://dx.doi.org/10.4310/CAG.2010.v18.n1.a5

Authors

Michel Boileau (Laboratoire Émile Picard, Université Paul Sabatier, Toulouse, France)

Steve Boyer (Départment de Mathematiques, Université du Québec à Montréal)

Alan W. Reid (Department of Mathematics, University of Texas, Austin)

Shicheng Wang (Department of Mathematics, Peking University, Beijing)

Abstract

It is conjectured that for each knot $K$ in $S^3$, thefundamental group of its complement surjects onto onlyfinitely many distinct knot groups. Applying charactervariety theory we obtain an affirmative solution of theconjecture for a class of small knots that includestwo-bridge knots.

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