On continuous extension of grafting maps

Details On continuous extension of grafting maps On continuous extension of grafting maps

2004-11-06

arxiv.org/abs/math/0411133v1

Trans. Amer. Math. Soc. 360 (2008), 3731-3749

Mathematics

Geometric Topology

24 pages, 2 figures

Scientific paper

10.1090/S0002-9947-08-04333-X

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg 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.

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