Double branched covers of theta-curves
| Autor: | Jules R. Metcalf-Burton, Jack S. Calcut |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Geometric Topology (math.GT) Primary 57M12 57M25 Secondary 57M35 57Q91 Mathematics::Geometric Topology 01 natural sciences Combinatorics Mathematics - Geometric Topology Prime knot 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Primality test Knot (mathematics) Mathematics |
| Zdroj: | Journal of Knot Theory and Its Ramifications. 25:1650046 |
| ISSN: | 1793-6527 0218-2165 |
| DOI: | 10.1142/s0218216516500462 |
| Popis: | 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. 8 pages, 5 figures. Results the same, proof of Lemma 2.2 simplified, Example 3.1 simplified, three references added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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