On continuous extension of grafting maps

Abstract

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.

24 pages, 2 figures

References in corpus (2)

• Exotic projective structures and quasifuchsian spaces II
• Projective structures with degenerate holonomy and the Bers density conjecture

Cited by in corpus (3)

• Exotic projective structures and quasifuchsian spaces II
• 2 π-grafting and complex projective structures, I
• 2π-grafting and complex projective structures with generic holonomy