On character varieties of two‐bridge knot groups

By M. L. Macasieb, Kathleen L. Petersen, Ronald van Luijk. 2009

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We find explicit models for the PSL2(ℂ)‐ and SL2(ℂ)‐character varieties of the fundamental groups of complements in 𝕊3 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 they are commensurable to a fibered knot complement in a ℤ/2ℤ‐homology sphere, resolving a conjecture of Hoste and Shanahan.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/9bffe9f51d8b3ab284cd6af28c805efe26e0f645