Grafting, pruning, and the antipodal map on measured laminations

Preprint, Other literature type English OPEN
Dumas, David;
(2005)

Grafting a measured lamination on a hyperbolic surface defines a self-map of Teichmuller space, which is a homeomorphism by a result of Scannell and Wolf. In this paper we study the large-scale behavior of pruning, which is the inverse of grafting. Specifically, for eac... View more
  • References (30)
    30 references, page 1 of 3

    [Bes] Mladen Bestvina. Degenerations of the hyperbolic space. Duke Math. J. 56(1988), 143-161.

    [CS] Marc Culler and Peter B. Shalen. Varieties of group representations and splittings of 3-manifolds. Ann. of Math. (2) 117(1983), 109-146.

    [D] David Dumas. Complex Projective Structures, Grafting, and Teichmu¨ller Theory. PhD thesis, Harvard University, May 2004.

    [FW] Benson Farb and Michael Wolf. Harmonic splittings of surfaces. Topology 40(2001), 1395-1414.

    [FLP] A. Fathi, F. Laudenbach, and V. Poenaru. Travaux de Thurston sur les surfaces, volume 66 of Ast´erisque. Soci´et´e Math´ematique de France, Paris, 1979. S´eminaire Orsay, With an English summary.

    [Gar] Frederick P. Gardiner. Teichmu¨ller theory and quadratic differentials. Pure and Applied Mathematics. John Wiley & Sons Inc., New York, 1987.

    [Har] Philip Hartman. On homotopic harmonic maps. Canad. J. Math. 19(1967), 673- 687.

    [HM] John Hubbard and Howard Masur. Quadratic differentials and foliations. Acta Math. 142(1979), 221-274.

    [KT] Yoshinobu Kamishima and Ser P. Tan. Deformation spaces on geometric structures. In Aspects of low-dimensional manifolds, pages 263-299. Kinokuniya, Tokyo, 1992.

    [Kap] Michael Kapovich. Hyperbolic manifolds and discrete groups. Birkh¨auser Boston Inc., Boston, MA, 2001.

  • Metrics
Share - Bookmark