The Sl(2, )-Character Variety of a Montesinos Knot

Abstract

For each Montesinos knot K , we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ 0 (K)⊔χ 1 ( K )⊔χ 2 ( K )⊔χ'( K ), where χ 0 ( K ) consists of trace-free characters χ 1 ( K ) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ 2 ( K ) is an algebraic curve, and χ'( K ) consists of finitely many points when K satisfies a generic condition.