The Topology of locally volume collapsed 3-Orbifolds

Faessler, Daniel (2011): The Topology of locally volume collapsed 3-Orbifolds. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

Abstract

In this thesis we study the geometry and topology of Riemannian 3-orbifolds which are locally volume collapsed with respect to a curvature scale. Our main result is that a sufficiently collapsed closed 3-orbifold without bad 2-suborbifolds satisfies Thurston’s Geometrization Conjecture. We also prove a version of this result with boundary. Kleiner and Lott indepedently and simultanously proved similar results ([KL11]). The main step of our proof is to construct a graph decomposition of sufficiently collapsed (closed) 3-orbifolds. We describe a coarse stratification of roughly 2-dimensional Alexandrov spaces which we then promote to a decomposition into suborbifolds for collapsed 3-orbifolds; this decomposition can then be reduced to a graph decomposition. We complete our proof by showing that graph orbifolds without bad 2-suborbifolds satisfy the Geometrization Conjecture.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik ; 500 Naturwissenschaften und Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 30. Juni 2011
• 1. Bericht­erstatter:in: Leeb, Bernhard