On the Algebraic Foundations of Bounded Cohomology.

Intro -- Contents -- Introduction and Main Results -- 1. Reconstructing the Burger-Monod Theory -- 2. More Functoriality -- 3. Discrete Groups -- 4. Amenable Groups -- 5. 1-Homology and Bounded Cohomology for Spaces -- 6. The Canonical Semi-Norm -- Part 1. Triangulated Categories -- Chapter I. Triangulated Categories -- 1. Definition and Elementary Properties -- 2. Triangle Functors -- Chapter II. The Derived Category of an Exact Category -- 1. Verdier Localization -- 2. The Derived Category of an Exact Category -- 3. Derived Functors -- Chapter III. Abstract Truncation: t-Structures and Hearts -- 1. Introduction -- 2. Abstract Truncation -- Part 2. Homological Algebra for Bounded Cohomology -- Chapter IV. Categories of Banach Spaces -- 1. The Bicomplete Category of Banach Spaces -- 2. The Additive Category of Banach Spaces -- Chapter V. Derived Categories of Banach G-Modules -- 1. Discrete Groups -- 2. Some Remarks on Topological Groups -- Part 3. Appendices -- Appendix A. Mapping Cones, Homotopy Push-Outs, Mapping Cylinders -- 1. The Mapping Cone -- Appendix B. Pull-Back of Exact Structures -- Appendix C. Model Categories -- 1. Statement of the Result -- 2. Proof of Theorem 1.2.2 -- 3. Remarks -- Appendix D. Standard Borel G-Spaces are Regular -- 1. Representations Associated to a Group Action -- Appendix E. The Existence of Bruhat Functions -- 1. Proper Group Actions -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.