Iterated grafting and holonomy lifts of Teichmuller space

作者：Hensel Sebastian W^*

来源：Geometriae Dedicata, 2011, 155(1): 31-67.

DOI：10.1007/s10711-011-9577-0

• Teichmuller theory
• Complex projective structures
• Grafting

Let X be a closed hyperbolic surface and lambda, eta be weighted geodesic multicurves which are short on X. We show that the iterated grafting along lambda and eta is close in the Teichmuller metric to grafting along a single multicurve which can be given explicitly in terms of lambda and eta. Using this result, we study the holonomy lifts gr (lambda) rho (X,lambda) of Teichmuller geodesics rho (X,lambda) for integral laminations lambda and show that all of them have bounded Teichmuller distance to the geodesic rho (X,lambda). We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences gr (n lambda) X and show that they converge geometrically to a punctured surface.

• 出版日期2011-12