Double branched covers of theta-curves
We prove a folklore theorem of 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. is prime, if and only if lifting the third arc of the theta-curve to the double branched cover over. produces a prime knot. We apply this result to Kinoshita's theta-curve.
Calcut, Jack S., and Jules R. Metcalf-Burton. 2016. "Double branched covers of theta-curves." Journal Of Knot Theory And Its Ramifications 25(8): 1-9.
World Scientific Publishing
Journal of Knot Theory and Its Ramifications
Theta-curve, Prime, Double branched cover, Equivariant Dehn's Iemma, Kinoshita's theta-curve