| (−2,3,7) pretzel knot | |
|---|---|
 |
|
| Arf invariant | 0 |
| Crosscap no. | 2 |
| Crossing no. | 12 |
| Hyperbolic volume | 2.828122 |
| Unknotting no. | 5 |
| Conway notation | [−2,3,7] |
| Dowker notation | 4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14 |
| D–T notation | 12n242 |
| Last / Next | 12n241 / 12n243 |
| Other | |
| hyperbolic, fibered, pretzel, reversible | |
In geometric topology, a branch of mathematics, the (−2, 3, 7) pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional surgery constructions.
Mathematical properties
The (−2, 3, 7) pretzel knot has 7 exceptional slopes, Dehn surgery slopes which give non-hyperbolic 3-manifolds. Among the enumerated knots, the only other hyperbolic knot with 7 or more is the figure-eight knot, which has 10. All other hyperbolic knots are conjectured to have at most 6 exceptional slopes.
Further reading
- Kirby, R., (1978). “Problems in low dimensional topology”, Proceedings of Symposia in Pure Math., volume 32, 272–312. (see problem 1.77, due to Gordon, for exceptional slopes)
External links
This article is adapted from “(−2,3,7) pretzel knot” on Wikipedia, written by its contributors, and used under CC BY-SA 4.0. Text on this page is available under the same licence. Source snapshot: Wikipedia via Kiwix, 2026-07-20.