\(SU(2)\)-representation spaces for two-bridge knots. (English) Zbl 0694.57003

Representation spaces of the fundamental groups of 2-bridge knot and link complements into SO(3) and SU(2) are described by real plane algebraic curves. The curves are investigated via their singularities and in certain cases proved to be rational. A simple proof is given for the fact that the fundamental group of any manifold resulting from \(S^ 3\) by Dehn surgery along a two-bridge knot possesses non-abelian homomorphic images in SO(3) and SU(2).
Reviewer: G.Burde


57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
20C32 Representations of infinite symmetric groups
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
14H99 Curves in algebraic geometry
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