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

@inproceedings{Farb2006AU2,
  title={A ug 2 00 7 The lower central series and pseudo-Anosov dilatations},
  author={Benson Farb and Christopher J. Leininger and Dan Margalit},
  year={2006}
}
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

References

Publications referenced by this paper.
Showing 1-10 of 32 references

Examples of pseudo-Anosov homeomorphisms with small dilatations

  • Hiroyuki Minakawa
  • J. Math. Sci. Univ. Tokyo,
  • 2006

Upper and lower bounds for the minimal positive entropy of pure braids

  • Won Taek Song
  • Bull. London Math. Soc.,
  • 2005

Knot Theory Ramifications

  • Won Taek Song, Ki Hyoung Ko, J JérômeE.Los.Entropiesofbraids.
  • 11(4):647–666,
  • 2002

McMullen . Polynomial invariants for fibered 3 - manifolds and Teichmüller geodesics for foliations

  • Hiroyuki Minakawa
  • Ann . Sci . École Norm . Sup . ( 4 )
  • 2000

Invent

  • Howard A. Masur, Yair N. Minsky. Geometry of the complex of curves. I. Hyperbolicity
  • Math., 138(1):103–149,
  • 1999

Similar Papers

Loading similar papers…