On continuous extensions of grafting maps
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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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2386243
Dedicated: To the memory of Professor Nobuyuki Suita