Character Varieties of Double Twist Links
نویسنده
چکیده
We compute both natural and smooth models for the SL2(C) character varieties of the two component double twist links, an infinite family of two-bridge links indexed as J(k, l). For each J(k, l), the component(s) of the character variety containing characters of irreducible representations are birational to a surface of the form C × C where C is a curve. The same is true of the canonical component. We compute the genus of this curve, and the degree of irrationality of the canonical component. We realize the natural model of the canonical component of the SL2(C) character variety of the J(3, 2m+ 1) links as the surface obtained from P × P as a series of blow-ups.
منابع مشابه
On Character Varieties of Two-bridge Knot Groups
We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if t...
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