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On continuous extensions of grafting maps


Author: Kentaro Ito
Journal: Trans. Amer. Math. Soc. 360 (2008), 3731-3749
MSC (2000): Primary 30F40; Secondary 57M50
DOI: https://doi.org/10.1090/S0002-9947-08-04333-X
Published electronically: January 29, 2008
MathSciNet review: 2386243
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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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Additional Information

Kentaro Ito
Affiliation: Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Email: itoken@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-08-04333-X
Keywords: Projective structures, quasifuchsian space, grafting
Received by editor(s): November 4, 2004
Received by editor(s) in revised form: October 17, 2005, and May 18, 2006
Published electronically: January 29, 2008
Dedicated: To the memory of Professor Nobuyuki Suita
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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