| 词条 | (−2,3,7) pretzel knot |
| 释义 |
| name= (−2,3,7) pretzel knot | practical name= | image= Pretzel knot.svg | caption= | arf invariant= 0 | bridge number= | crosscap number= 2 | crossing number= 12 | hyperbolic volume= 2.828122088 | linking number= | stick number= | unknotting number= 5 | conway_notation= [7;-2 1;2] | dowker notation= 4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14 | d-t name= 12n242 | last crossing= 12n241 | last order= | next crossing= 12n243 | next order= | alternating= | class= hyperbolic | fibered= fibered | pretzel= pretzel | slice= | symmetry= reversible | tricolorable= }} 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 propertiesThe (−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. Further reading{{refbegin}}
External links
3 : 3-manifolds|4-manifolds|2.82812 hyperbolic volume knots and links |
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