Trisha Shetty (Editor)

(−2,3,7) pretzel knot

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

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.


(−2,3,7) pretzel knot Wikipedia