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.
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Authors supply an estimate for fixed points of pseudo-Anosov maps and prove that, under strong irreducibility, log of the count is coarsely the Teichmuller length, plus volume-homology inequalities for mapping tori.
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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.
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On fixed points of pseudo-Anosov maps
Authors supply an estimate for fixed points of pseudo-Anosov maps and prove that, under strong irreducibility, log of the count is coarsely the Teichmuller length, plus volume-homology inequalities for mapping tori.