(-2, 3, 7) pretzel knot
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In geometric topology, the (-2, 3, 7) pretzel knot, sometimes called the Fintushel-Stern knot, is an important example of a pretzel knot which exhibit various interesting phenomena under three-dimensional and four-dimensional surgery constructions.
[edit] Mathematical properties
- The (-2, 3, 7) pretzel knot has 7 exceptional slopes, Dehn surgery slopes which give non-hyperbolic 3-manifolds. 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.
[edit] References
- R. Kirby, Problems in low-dimensional topology, (see problem 1.77, due to Gordon, for exceptional slopes)
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