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 |
| Type of entry: |
Primary publication |
| Title: |
The Invariant Complex Structure on the Homogeneous Space Diff(S1)/Rot(S1) |
| Language: |
English |
| Referees: |
Püttmann, PD Dr. Thomas |
| Advisors: |
Neeb, Prof. Dr. Karl-Hermann |
| Date: |
11 July 2007 |
| Place of Publication: |
Darmstadt |
| Publisher: |
Technische Universität |
| Refereed: |
23 January 2007 |
| URL / URN: |
urn:nbn:de:tuda-tuprints-8468 |
| 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. |
| 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 |
|
| 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 |
| Alternative keywords: |
| Alternative keywords | Language |
|---|
| 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 Theorem | English |
|
| Classification DDC: |
500 Science and mathematics > 510 Mathematics |
| Divisions: |
04 Department of Mathematics |
| Date Deposited: |
17 Oct 2008 09:22 |
| Last Modified: |
26 Aug 2018 21:25 |
| PPN: |
|
| Referees: |
Püttmann, PD Dr. Thomas |
| Refereed / Verteidigung / mdl. Prüfung: |
23 January 2007 |
| Alternative keywords: |
| Alternative keywords | Language |
|---|
| 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 Theorem | English |
|
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