| (−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 | |
Ingeometric topology, a branch ofmathematics, the(−2, 3, 7) pretzel knot, sometimes called theFintushel–Stern knot (afterRon Fintushel andRonald J. Stern), is an important example of apretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensionalsurgery constructions.
The (−2, 3, 7) pretzel knot has 7exceptional slopes,Dehn surgery slopes which give non-hyperbolic 3-manifolds. Among the enumerated knots, the only other hyperbolic knot with 7 or more is thefigure-eight knot, which has 10. All other hyperbolic knots are conjectured to have at most 6 exceptional slopes.
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