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Teichmuller mapping class group of the universal hyperbolic solenoid
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UNSPECIFIED (2006) Teichmuller mapping class group of the universal hyperbolic solenoid. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 358 (6). pp. 2637-2650. ISSN 0002-9947.
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Abstract
We show that the homotopy class of a quasiconformal self-map of the universal hyperbolic solenoid H-infinity is the same as its isotopy class and that the uniform convergence of quasiconformal self-maps of H-infinity to the identity forces them to be homotopic to conformal maps. We identify a dense subset of T (H-infinity) such that the orbit under the base leaf preserving mapping class group MCG(BLP) (H-infinity) of any point in this subset has accumulation points in the Teichmuller space T (H-infinity). Moreover, we show that finite subgroups of MCG(BLP) (H-infinity) are necessarily cyclic and that each point of T (H-infinity) has an infinite isotropy subgroup in MCGBLP (H-infinity).
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | ||||
Publisher: | AMER MATHEMATICAL SOC | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 2006 | ||||
Dates: |
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Volume: | 358 | ||||
Number: | 6 | ||||
Number of Pages: | 14 | ||||
Page Range: | pp. 2637-2650 | ||||
Publication Status: | Published |
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