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| Dateien: |
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| Zitierfähiger Link (URI): |
http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-6662
http://hdl.handle.net/10900/48427 http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-484279 http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-484278 |
| Dokumentart: | Dissertation |
| Erscheinungsdatum: | 2002 |
| Sprache: | Deutsch |
| Fakultät: | 7 Mathematisch-Naturwissenschaftliche Fakultät |
| Fachbereich: | Sonstige - Mathematik und Physik |
| Gutachter: | Leeb, Bernhard |
| Tag der mündl. Prüfung: | 2002-12-19 |
| DDC-Klassifikation: | 510 - Mathematik |
| Schlagworte: | Niederdimensionale Topologie , Mannigfaltigkeit / Dimension 3 , Einsteinsche Mannigfaltigkeit , Hyperbolische Mannigfaltigkeit |
| Freie Schlagwörter: |
Geometrisierung von 3-Mannigfaltigkeiten , Deformationen von Kegelmannigfaltigkeitsstrukturen Geometric topology , Geometrization of 3-manifolds , Deformations of cone-manifold structures
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| Lizenz: | http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=de http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=en |
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Inhaltszusammenfassung:
We investigate local rigidity of 3-dimensional cone-manifolds with cone-angles not larger than $pi$. Under this cone-angle restriction the singular locus is a trivalent graph. We obtain local rigidity in the hyperbolic and the spherical case. From a technical point of view the main result is a vanishing theorem for $L^2$-cohomology of the smooth part of the cone-manifold with coefficients in the flat vectorbundle of infinitesimal isometries. From this local rigidity is deduced by an analysis of the variety of representations.
Abstract:
We investigate local rigidity of 3-dimensional cone-manifolds with cone-angles not larger than $pi$. Under this cone-angle restriction the singular locus is a trivalent graph. We obtain local rigidity in the hyperbolic and the spherical case. From a technical point of view the main result is a vanishing theorem for $L^2$-cohomology of the smooth part of the cone-manifold with coefficients in the flat vectorbundle of infinitesimal isometries. From this local rigidity is deduced by an analysis of the variety of representations.