| (−2,3,7) pretzel knot | |
| Arf Invariant: | 0 |
| Crosscap Number: | 2 |
| Crossing Number: | 12 |
| Hyperbolic Volume: | 2.828122 |
| Unknotting Number: | 5 |
| Conway Notation: | [−2,3,7] |
| Dowker Notation: | 4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14 |
| D-T Name: | 12n242 |
| Last Crossing: | 12n241 |
| Last Order: | |
| Next Crossing: | 12n243 |
| Next Order: | |
| Class: | hyperbolic |
| Fibered: | fibered |
| Pretzel: | pretzel |
| Symmetry: | 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.
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.