Doctor of Philosophy (PhD)
A group G is called left-orderable if one can find a total order on G, which is preserved under left multiplication. In this paper we first give a sufficient condition for the fundamental group of the nth cyclic branched cover of the three sphere over a prime knot K to be left-orderable, in terms of representations of the knot group. Then we make use of this criterion to study the left-orderability of fundamental groups of cyclic branched covers over two-bridge knots and satellite knots.
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Hu, Ying, "Left-orderability, Cyclic Branched Covers and Representations of the Knot Group" (2015). LSU Doctoral Dissertations. 3178.