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.
Atoroidal surface bundles
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abstract
We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes of purely pseudo-Anosov surface subgroups of mapping class groups of closed surfaces. This gives the first examples of compact atoroidal surface bundles over surfaces.
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math.GT 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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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.