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Riley's conjecture on SL(2,R) representations of 2-bridge knots

Riley's conjecture on SL(2,R) representations of 2-bridge knots

We prove a conjecture of Riley on [Formula: see text] representations of 2-bridge knot groups. As a consequence we show that if [Formula: see text] is a 2-bridge knot with non-zero signature, then the fundamental group of the [Formula: see text]-fold cyclic branched cover of [Formula: see text] is left-orderable …