On continuous extensions of grafting maps

Ito, Kentaro

doi:10.1090/S0002-9947-08-04333-X

On continuous extensions of grafting maps
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Trans. Amer. Math. Soc. 360 (2008), 3731-3749 Request permission

Abstract:

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg (preprint) to all $b$-groups. In this paper, we show that the extended grafting maps behave as continuous maps for every sequence which converges “standardly” to a boundary group, although the maps are not continuous in general. As a consequence of this result, we extend Goldman’s grafting theorem for quasifuchsian groups to all boundary $b$-groups.

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