Double branched covers of theta-curves

2015/09/25 by Calcut, Jack S., Metcalf-Burton, Jules R. · 2 citations
#57M25 #57Q91 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M12 #Secondary 57M35

paper · doi:10.48550/arxiv.1509.07788

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.

Cited by

• Prime theta-curves on minimal genus Seifert surfaces
• Structure and classification of torus theta-curves

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