Faessler, Daniel (2011): The Topology of locally volume collapsed 3Orbifolds. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

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Abstract
In this thesis we study the geometry and topology of Riemannian 3orbifolds which are locally volume collapsed with respect to a curvature scale. Our main result is that a sufficiently collapsed closed 3orbifold without bad 2suborbifolds 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) 3orbifolds. We describe a coarse stratification of roughly 2dimensional Alexandrov spaces which we then promote to a decomposition into suborbifolds for collapsed 3orbifolds; this decomposition can then be reduced to a graph decomposition. We complete our proof by showing that graph orbifolds without bad 2suborbifolds satisfy the Geometrization Conjecture.
Item Type:  Thesis (Dissertation, LMU Munich) 

Subjects:  600 Natural sciences and mathematics > 510 Mathematics 600 Natural sciences and mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  30. June 2011 
1. Referee:  Leeb, Bernhard 
Persistent Identifier (URN):  urn:nbn:de:bvb:19131850 
MD5 Checksum of the PDFfile:  871c3cdd2ecb947d6637f000de4f153d 
Signature of the printed copy:  0001/UMC 19556 
ID Code:  13185 
Deposited On:  07. Jul 2011 07:25 
Last Modified:  16. Oct 2012 08:51 