| Arf invariant 0 Crossing no. 12 Unknotting no. 5 | Crosscap no. 2 Hyperbolic volume 2.828122088 Conway notation [7;-2 1;2] | |
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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.
References
(−2,3,7) pretzel knot Wikipedia(Text) CC BY-SA