Perko pair
From Wikipedia, the free encyclopedia
| Perko pair | |
|---|---|
| Arf invariant | 1 |
| Braid length | 10 |
| Braid no. | 3 |
| Bridge no. | 3 |
| Crosscap no. | 2 |
| Crossing no. | 10 |
| Hyperbolic volume | 5.63877 |
| Unknotting no. | 3 |
| Conway notation | [3:-20:-20] |
| A-B notation | 10161/10162 |
| Dowker notation | 4, 12, -16, 14, -18, 2, 8, -20, -10, -6 |
| Last /Next | 10160 / 10162 |
| Other | |
| hyperbolic, fibered, prime, reversible | |
In the mathematical theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Rolfsen's knot table, this supposed pair of distinct knots is labeled 10161 and 10162. In 1974, while working to complete the Tait–Little knot tables of knots up to 10 crossings (dating from the late 19th century), Perko found the duplication in C. N. Little's table. This duplication had been missed by John Horton Conway several years before in his knot table and subsequently found its way into Rolfsen's table.
- The Perko pair
-
10161 -
10162
Further reading
- Kenneth A. Perko Jr., On the classification of knots. Proc. Amer. Math. Soc. 45 (1974), 262—266.
- Dale Rolfsen, Knots and Links (see Appendix C for the knot table), 1976, ISBN 0-914098-16-0
External links
- "10_161", The Knot Atlas.
| |||||||||||||||||||||||
This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.