Fuchsian germs.
Item
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Title
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Fuchsian germs.
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Identifier
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AAI9807933
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identifier
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9807933
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Creator
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Gendron, Timothy Mooney.
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Contributor
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Adviser: Dennis P. Sullivan
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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We prove in this thesis the following uniformization.;Theorem. Let L be an irreducible Riemann surface lamination. Then there exists a space (H) consisting of a family of hyperbolic half-planes, and a groupoid {dollar}\lbrack\Gamma\rbrack{dollar} consisting of equivalence classes of sequences of elements of {dollar}PSL(2,{dollar}R), such that {dollar}\lbrack\Gamma\rbrack{dollar} acts on (H) with quotient (H) /{dollar}\lbrack\Gamma\rbrack{dollar} an irreducible hyperbolic Riemann surface lamination isomorphic to L.;The groupoid {dollar}\lbrack\Gamma\rbrack{dollar} is called a Fuchsian germ. When the construction is applied to a Riemann surface uniformized by Fuchsian group {dollar}\Gamma,{dollar} one obtains {dollar}\sp{lcub}\*{rcub}\Gamma{dollar} = the ultrapower of {dollar}\Gamma{dollar} with respect to some ultrafilter. The Fuchsian germs of any inverse limit solenoid, as well as the Feigenbaum solenoid, are calculated and are seen to be groups.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
