Inspired by ``the trefoil knot is knotted" answer, how about the fact that Reidemeister moves generate isotopy of PL knots? This is pretty obvious but a full proof requires a lot of machinery. Indeed, the proof was not known to Reidemeister, who took the fact that his eponymous moves generate isotopy as an unproven axiom. (See Daniel Moskovich's comment.)
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Inspired by ``the trefoil knot is knotted" answer, how about the fact that Reidemeister moves generate isotopy of PL knots? This is pretty obvious but a full proof requires a lot of machinery. Indeed, the proof was not known to Reidemeister, who took the fact that his eponymous moves generate isotopy as an unproven axiom. |
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