Constructing geometrically infinite groups on boundaries of deformation spaces
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- OHSHIKA Ken’ichi
- Department of Mathematics, Graduate School of Science, Osaka University
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Abstract
Consider a geometrically finite Kleinian group G without parabolic or elliptic elements, with its Kleinian manifold M=(H3∪ΩG)⁄G. Suppose that for each boundary component of M, either a maximal and connected measured lamination in the Masur domain or a marked conformal structure is given. In this setting, we shall prove that there is an algebraic limit Γ of quasi-conformal deformations of G such that there is a homeomorphism h from IntM to H3⁄Γ compatible with the natural isomorphism from G to Γ, the given laminations are unrealisable in H3⁄Γ, and the given conformal structures are pushed forward by h to those of H3⁄Γ. Based on this theorem and its proof, in the subsequent paper, the Bers-Thurston conjecture, saying that every finitely generated Kleinian group is an algebraic limit of quasi-conformal deformations of minimally parabolic geometrically finite group, is proved using recent solutions of Marden’s conjecture by Agol, Calegari-Gabai, and the ending lamination conjecture by Minsky collaborating with Brock, Canary and Masur.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 61 (4), 1261-1291, 2009
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390001205116268288
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- NII Article ID
- 10026998734
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 10406445
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed