A ug 2 00 7 The lower central series and pseudo-Anosov dilatations

  title={A ug 2 00 7 The lower central series and pseudo-Anosov dilatations},
  author={Benson Farb and Christopher J. Leininger and Dan Margalit},
The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface Sg of genus g. Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov homeomorphism of Sg tends to zero at the rate 1/g. We consider here the smallest dilatation of any pseudoAnosov homeomorphism of Sg acting trivially on Γ/Γk, the quotient of Γ = π1(Sg) by the k term of its lower central series, k ≥ 1. In contrast to Penner’s asymptotics… CONTINUE READING


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