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  "body": "\n## Example\n\nThe *Conway knot* is the prime [[knot|QYEAZTYGPT]] with $11$ crossings listed as $11n34$ in the knot tables, named after John Horton Conway.\nIt is obtained from the Kinoshita–Terasaka knot, another $11$-crossing knot, by a mutation.\nA mutation cuts out a ball that meets the knot in two arcs, rotates the ball by a half turn, and glues it back.\nThe result is again a knot, but in general not an equivalent one.\n\n## Remarks\n\nMutation does not change many [[knot invariants|GZQ5ZE3X6G]].\nThe Conway knot and the Kinoshita–Terasaka knot have the same [[Jones polynomial|4SPC17FPXE]], the same HOMFLY polynomial, and both have [[Alexander polynomial|JKA25KDPQP]] equal to $1$, like the [[unknot|1TQ06R4Q66]].\nThey are still different knots: the Conway knot has genus $3$, while the Kinoshita–Terasaka knot has genus $2$, as shown by David Gabai.\nSince its Alexander polynomial is $1$, the Conway knot is topologically [[slice|P68G28E4AD]], by a theorem of Michael Freedman.\nThe Kinoshita–Terasaka knot is smoothly slice.\nLisa Piccirillo proved in 2020 that the Conway knot is not smoothly slice, which answered a question that had been open for about fifty years.\n\n## Explanations\n\n### L1 human\n\nThe Conway knot is a knot with eleven crossings that fools many of the standard tests.\nIts polynomial invariants agree with those of a close relative, and its Alexander polynomial even agrees with that of the unknot.\nIt became famous when a graduate student, Lisa Piccirillo, settled whether it bounds a smooth disk in four-dimensional space.\n",
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