分野別セミナー

I will talk about an application of irreducibility of SL(2,C)-character varieties
of knot groups to a partial ordering on the set of prime knots. The irreducibility,
combined with a result in the paper of Boileau, Boyer, Reid and Wang
[Simon's conjecture for 2-bridge knots, Comm. Anal. Geom. 18 (2010) 121-143]
or Ohtsuki, Riley and Sakuma [Epimorphisms between 2-bridge link groups,
Geom. Topol. Monogr. 14 (2008) 417-450], gives the minimality of infinitely many

twist knots for the partial order.

This talk involves the definition and some examples of the partial
ordering of knots,
a quick review of SL(2,C)-character varieties of knot groups, a proof and
an application of the result of Boileau et al., Chebyshev polynomials and
an easy computer experiment etc.



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