Double branched covers of theta-curves

被引：5
|
作者：
Calcut, Jack S. [1 ]
Metcalf-Burton, Jules R. [2 ]
机构：
[1] Oberlin Coll, Dept Math, Oberlin, OH 44074 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2016年 / 25卷 / 08期
关键词：
Theta-curve; prime; double branched cover; equivariant Dehn lemma; Kinoshita's theta-curve;
D O I：
10.1142/S0218216516500462
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：9
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