Lokale Starrheit 3-dimensionaler Kegelmannigfaltigkeiten

DSpace Repository


Dateien:

URI: http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-6662
http://hdl.handle.net/10900/48427
Dokumentart: Dissertation
Date: 2002
Language: German
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Sonstige - Mathematik und Physik
Advisor: Leeb, Bernhard
Day of Oral Examination: 2002-12-19
DDC Classifikation: 510 - Mathematics
Keywords: Niederdimensionale Topologie , Mannigfaltigkeit / Dimension 3 , Einsteinsche Mannigfaltigkeit , Hyperbolische Mannigfaltigkeit
Other Keywords: Geometrisierung von 3-Mannigfaltigkeiten , Deformationen von Kegelmannigfaltigkeitsstrukturen
Geometric topology , Geometrization of 3-manifolds , Deformations of cone-manifold structures
License: Publishing license including print on demand
Order a printed copy: Print-on-Demand
Show full item record

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.

This item appears in the following Collection(s)