Double branched covers of theta-curves

Jack S. Calcut; Jules R. Metcalf-Burton

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arXiv · 1509.07788

Double branched covers of theta-curves

Jack S. Calcut·Jules R. Metcalf-Burton

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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.

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Jack S. Calcut, Jules R. Metcalf-Burton. 2016-02-27. Double branched covers of theta-curves. https://arxiv.org/abs/1509.07788

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