Double branched covers of theta-curves-Reference-Cited by-同舟云学术

Double branched covers of theta-curves

Published:2016-07 Issue:08 Volume:25 Page:1650046
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Calcut Jack S.¹,Metcalf-Burton Jules R.²

Affiliation:

1. Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA

2. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

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 [Formula: see text] is prime, if and only if lifting the third arc of the theta-curve to the double branched cover over [Formula: see text] produces a prime knot. We apply this result to Kinoshita’s theta-curve.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216516500462

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