Tuesday, 18 November 2008

gn.general topology - SU(2) representations of alternating knot groups

This looks like a good place to start from (if you haven't already read it)



MR2488756 (2009m:57024) Nagasato, Fumikazu . Finiteness of a section of the rmSL(2,BbbC)-character variety
of the knot group.
Kobe J. Math. 24 (2007), no. 2, 125--136.



This paper shows that for any knot, there are only finitely many irreducible metabelian characters in the rmSL(2,bfC) character variety. It is also shown that the number of conjugacy classes is given by a simple formula involving the Alexander polynomial. In the context of two bridge knots, there are inequalities involving the A-polynomial of the knot. Results of this nature were previously obtained by X. S. Lin [Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 3, 361--380; MR1852950 (2003f:57018)] for rmSU(2) representations.



This paper can be found at www.math.titech.ac.jp/~fukky/metabelian.pdf

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