Left-orderability, Cyclic Branched Covers and Representations of the Knot Group

Identifier

etd-06022015-174920

Author

Ying Hu, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

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.

Date

2015

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Hu, Ying, "Left-orderability, Cyclic Branched Covers and Representations of the Knot Group" (2015). LSU Doctoral Dissertations. 3178.
https://repository.lsu.edu/gradschool_dissertations/3178

Committee Chair

Dasbach, Oliver

DOI

10.31390/gradschool_dissertations.3178