Riley's Conjecture and cyclic branched covers of 2-bridge knots
Cameron Gordon (Austin)
Monday 27th February, 2017 16:00-17:00 Maths 204
In the early 1970's Riley studied certain representations of 2-bridge knot groups in SL(2,F) for various fields F. On the basis of computer calculations he conjectured that the number of such
representations in SL(2,R) is at least half the absolute value of the signature sigma(K) of K. We will prove this conjecture, and show that it implies that if K is a 2-bridge knot with non-zero sigma(K), then the fundamental group of the n-fold cyclic branched cover of K is left-orderable for n sufficiently large.