Abstract
We study representations of the knot groups of twist knots into . The set of nonabelian representations of a twist knot is described as the zero set in of a polynomial , where is the trace of a meridian. We prove some properties of . In particular, we prove that is irreducible over . As a consequence, we obtain an alternative proof of a result of Hoste and Shanahan that the degree of the trace field is precisely two less than the minimal crossing number of a twist knot.
Citation
James C. Dean. Anh T. Tran. "On nonabelian representations of twist knots." Involve 9 (5) 831 - 838, 2016. https://doi.org/10.2140/involve.2016.9.831
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