Bühler T. On the algebraic foundations of bounded cohomology. - Providence: American Mathematical Society, 2011. - xxi, 97 p.: ill. - (Memoirs of the American Mathematical Society; vol.214, N 1006.). - Bibliogr.: p.95-97. - ISBN 978-0-8218-5311-5; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Introduction and Main Results ................................. vii 1 Reconstructing the Burger-Monod Theory .................... viii 2 More Functoriality ........................................ xiii 3 Discrete Groups ............................................ xiv 4 Amenable Groups ............................................ xvi 5 ℓ1-Homology and Bounded Cohomology for Spaces ............. xviii 6 The Canonical Semi-Norm ..................................... xx Part 1 Triangulated Categories ................................. 1 Chapter I Triangulated Categories ............................. 3 1 Definition and Elementary Properties ......................... 3 2 Triangle Functors ........................................... 14 Chapter II The Derived Category of an Exact Category .......... 17 1 Verdier Localization ........................................ 17 2 The Derived Category of an Exact Category ................... 24 3 Derived Functors ............................................ 26 Chapter III Abstract Truncation: t-Structures and Hearts ....... 31 1 Introduction ................................................ 31 2 Abstract Truncation ......................................... 36 Part 2 Homological Algebra for Bounded Cohomology ............. 45 Chapter IV Categories of Banach Spaces ........................ 47 1 The Bicomplete Category of Banach Spaces .................... 47 2 The Additive Category of Banach Spaces ...................... 54 Chapter V Derived Categories of Banach G-Modules ............. 63 1 Discrete Groups ............................................. 63 2 Some Remarks on Topological Groups .......................... 70 Part 3 Appendices ............................................. 73 Appendix A Mapping Cones, Homotopy Push-Outs, Mapping Cylinders ...................................................... 75 1 The Mapping Cone ............................................ 75 Appendix B Pull-Back of Exact Structures ...................... 79 Appendix C Model Categories ................................... 81 1 Statement of the Result ..................................... 81 2 Proof of Theorem 1.2.2 ...................................... 83 3 Remarks ..................................................... 86 Appendix D Standard Borel G-Spaces are Regular ................ 87 1 Representations Associated to a Group Action ................ 87 Appendix E The Existence of Bruhat Functions .................. 91 1 Proper Group Actions ........................................ 91 Bibliography ................................................... 95