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On continuous extension of grafting maps

By Kentaro Ito


The definition of the grafting operation for quasifuchsian groups is extended by Bromberg [Br] to all b-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every “standard ” convergent sequence to a convergent sequence. As a consequence of this result, we extend Goldman’s grafting theorem for quasifuchsian groups to all boundary b-groups.

Year: 2004
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