2018/01/08 by Ba, Idrissa
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1801.02692
We show that the 3-fold cyclic branched cover of any genus 2 two-bridge knot K[-2q,2s,-2t,2l] is an L-space and its fundamental group is not left-orderable. Therefore the family of 3-fold cyclic branched cover of any genus 2 two-bridge knot K[-2q,2s,-2t,2l] verifies the L-space conjecture. We also show that if K[2k,-2l] is a 2-bridge knot with k≥ 2, l>0, then the fundamental group of the 5-fold cyclic branched cover of K[2k,-2l] is not left-orderable, which will complete the proof that the fundamental group of the 5-fold cyclic branched cover of any genus one two-bridge knot is not left-orderable.