(−2,3,7) pretzel knot | |
---|---|

Arf invariant | 0 |

Crosscap no. | 2 |

Crossing no. | 12 |

Hyperbolic volume | 3.66386^{[1]} |

Unknotting no. | 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 /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.

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.

**^**Agol, Ian (2010), "The minimal volume orientable hyperbolic 2-cusped 3-manifolds", Proceedings of the American Mathematical Society, 138 (10): 3723–3732, arXiv:0804.0043, doi:10.1090/S0002-9939-10-10364-5, MR 2661571.

- 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)