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The Invariant Complex Structure on the Homogeneous Space Diff(S1)/Rot(S1)

Hofmann-Kliemt, Matthias (2007):
The Invariant Complex Structure on the Homogeneous Space Diff(S1)/Rot(S1).
Darmstadt, Technische Universität, TU Darmstadt, [Online-Edition: urn:nbn:de:tuda-tuprints-8468],
[Ph.D. Thesis]

Abstract

Let Diff(S1) be the Frechet-Lie group of orientation preserving diffeomorphisms of the unit circle S1. Let Rot(S1) be the subgroup of metric preserving rotations. The homogeneous space M=Diff(S1)/Rot(S1) has a structure of a Frechet manifold. In this thesis, it is shown that on M there exists exactly one complexe structure up to sign which is invariant under the action of Diff(S1) on M.

Item Type: Ph.D. Thesis
Erschienen: 2007
Creators: Hofmann-Kliemt, Matthias
Title: The Invariant Complex Structure on the Homogeneous Space Diff(S1)/Rot(S1)
Language: English
Abstract:

Let Diff(S1) be the Frechet-Lie group of orientation preserving diffeomorphisms of the unit circle S1. Let Rot(S1) be the subgroup of metric preserving rotations. The homogeneous space M=Diff(S1)/Rot(S1) has a structure of a Frechet manifold. In this thesis, it is shown that on M there exists exactly one complexe structure up to sign which is invariant under the action of Diff(S1) on M.

Place of Publication: Darmstadt
Publisher: Technische Universität
Uncontrolled Keywords: Kreisgruppe, Diffeomorphismengruppe, homogener Raum, invariante komplexe Struktur, fast-komplexe Struktur, Frechet-Mannigfaltigkeit, zahmer Frechet-Raum, quasikonforme Abbildung, Birkhoff-Zerlegung, Satz von Nash-Moser, Hilbert-Transformation, Riemannscher Abbildungssatz
Divisions: 04 Department of Mathematics
Date Deposited: 17 Oct 2008 09:22
Official URL: urn:nbn:de:tuda-tuprints-8468
License: only the rights of use according to UrhG
Referees: Püttmann, PD Dr. Thomas
Refereed / Verteidigung / mdl. Prüfung: 23 January 2007
Alternative keywords:
Alternative keywordsLanguage
circle group, diffeomorphism group, homogeneous space, invariant complex structure, Frechet-manifold, tame Frechet-space, quasiconformal mapping, Birkhoff-decomposition, Nash-Moser-Theorem, Hilbert transformation, Riemann Mapping TheoremEnglish
Alternative Abstract:
Alternative abstract Language
Es sei Diff(S1) die Frechet-Lie-Gruppe der orientierungserhaltenden Diffeomorphismen des Einheitskreises. Sei Rot(S1) die Untergruppe der starren Rotationen. Dann ist der homogene Raum M=Diff(S1)/Rot(S1) eine Frechet-Mannigfaltigkeit. In dieser Arbeit wird gezeigt, dass es auf M bis auf ein Vorzeichen genau eine komplexe Struktur gibt, die unter der Wirkung von Diff(S1) invariant ist.German
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