Reductions, resolutions and the copolarity of isometric group actions [Elektronische Ressource] / vorgelegt von Frederick Magata

MathematikReductions, Resolutionsand the Copolarityof Isometric Group ActionsInaugural-Dissertationzur Erlangung des akademischen Grades einesDoktors der Naturwissenschaftendurch den Fachbereich Mathematik und Informatikder Westf¨alischen Wilhelms-Universit¨at Munster¨vorgelegt vonFrederick Magataaus Neuss- 2008 -Dekan: Prof. Dr. Dr. h.c. Joachim CuntzErster Gutachter: Prof. Dr. Linus KramerZweiter Gutachter: Prof. Dr. Claudio GorodskiTag der mundlic¨ hen Prufung:¨ 06.05.2008Tag der Promotion: 06.05.2008ContentsIntroduction 5Chapter 1. Fat Sections, Fat Weyl Groups and the Copolarity of IsometricActions 9Chapter 2. Structure Theory of Fat Sections and Reductions 132.1. Properties of Reductions 132.2. Copolarity and Reductions of the Slice Representation 162.3. Stability of Copolarity under Reductions 182.4. A Remark on Variational Completeness and Co-Completeness 192.5. Decomposition of Killing Fields and Adapted Metrics 232.6. A Generalization of Weyl’s Integration Formula 272.7. On a Generalization of Chevalley’s Restriction Theorem 34Chapter 3. Global Resolutions of Isometric Actions with Respect to Fat Sections 37Chapter 4. Copolarity of Singular Riemannian Foliations 43Chapter 5. Copolarity of Actions induced by Polar Actions on Symmetric Spaces 45Chapter 6. An Infinite Dimensional Isometric Action 51Chapter 7.