Title

Double branched covers of theta-curves

Abstract

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.

Publisher

World Scientific Publishing

Publication Date

7-1-2016

Publication Title

Journal of Knot Theory and Its Ramifications

Department

Mathematics

Document Type

Article

DOI

10.1142/S0218216516500462

Keywords

Theta-curve, Prime, Double branched cover, Equivariant Dehn's Iemma, Kinoshita's theta-curve

Language

English

Format

text

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