Double branched covers of theta-curves
Geometric Topology
2016-03-01 v2
Abstract
We prove a folklore theorem of W. Thurston which provides necessary and sufficient conditions for primality of a certain class of theta-curves. Namely, a theta-curve in the 3-sphere with an unknotted constituent knot U is prime if and only if lifting the third arc of the theta-curve to the double branched cover over U produces a prime knot. We apply this result to Kinoshita's theta-curve.
Keywords
Cite
@article{arxiv.1509.07788,
title = {Double branched covers of theta-curves},
author = {Jack S. Calcut and Jules R. Metcalf-Burton},
journal= {arXiv preprint arXiv:1509.07788},
year = {2016}
}
Comments
8 pages, 5 figures. Results the same, proof of Lemma 2.2 simplified, Example 3.1 simplified, three references added