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On continuous extensions of grafting maps
Author(s):
Kentaro
Ito
Journal:
Trans. Amer. Math. Soc.
360
(2008),
3731-3749.
MSC (2000):
Primary 30F40;
Secondary 57M50
Posted:
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  -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  -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:
10.1090/S0002-9947-08-04333-X
PII:
S 0002-9947(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
Posted:
January 29, 2008
Dedicated:
To the memory of Professor Nobuyuki Suita
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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