(−2,3,7) pretzel knot

Type of mathematical knot (−2,3,7) pretzel knot Pretzel knot.svg 0 2 12 2.828122 5 [−2,3,7] 4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14 12n242 12n241   12n243   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. thumbnail|center|A pretzel (−2,3,7) pretzel knot. 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 K12n242 Category:3-manifolds