Existence of a type-preserving homomorphism from the figure-eight knot complement fundamental group to the mapping class group of the thrice-punctured torus, yielding first examples of compact atoroidal surface bundles over surfaces.
Hatcher.Algebraic topology
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Atoroidal surface bundles
Existence of a type-preserving homomorphism from the figure-eight knot complement fundamental group to the mapping class group of the thrice-punctured torus, yielding first examples of compact atoroidal surface bundles over surfaces.