Manifolds and cell complexes Knot theory Example
Conway knot
Example
The Conway knot is the prime knot with crossings listed as in the knot tables, named after John Horton Conway. It is obtained from the Kinoshita–Terasaka knot, another -crossing knot, by a mutation. A mutation cuts out a ball that meets the knot in two arcs, rotates the ball by a half turn, and glues it back. The result is again a knot, but in general not an equivalent one.
Remarks
Mutation does not change many knot invariants. The Conway knot and the Kinoshita–Terasaka knot have the same Jones polynomial, the same HOMFLY polynomial, and both have Alexander polynomial equal to , like the unknot. They are still different knots: the Conway knot has genus , while the Kinoshita–Terasaka knot has genus , as shown by David Gabai. Since its Alexander polynomial is , the Conway knot is topologically slice, by a theorem of Michael Freedman. The Kinoshita–Terasaka knot is smoothly slice. Lisa Piccirillo proved in 2020 that the Conway knot is not smoothly slice, which answered a question that had been open for about fifty years.
Further reading
About this page
| Tag | ZSAMVFPWN6 |
|---|---|
| URI | m2://ZSAMVFPWN6 |
| Kind | example |
| Writing | W0 stub |
| MSC | 57K10 |
| Instance of | Knot |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
No page links to this page yet.