A Tool Kit for Groupoid C*-Algebra

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Contents
Introduction
Chapter 1. From Groupoid to Algebra
1.1. Sectionformat {Preliminaries}{1}
1.2. Sectionformat {Getting Started}{1}
1.3. Sectionformat {Haar Systems}{1}
1.4. Sectionformat {Building cs -Algebras}{1}
Chapter 2. Groupoid Actions and Equivalence
2.1. Sectionformat {Groupoid Actions}{1}
2.2. Sectionformat {The Mackey-Glimm-Ramsay Dichotomy}{1}
2.3. Sectionformat {Equivalence}{1}
2.4. Sectionformat {Generalized Morphisms}{1}
2.5. Sectionformat {Linking Groupoids}{1}
2.6. Sectionformat {The Equivalence Theorem}{1}
2.7. Sectionformat {Some Important Examples}{1}
2.8. Sectionformat {Transitive Groupoid cs -Algebras}{1}
Chapter 3. Measure Theory
3.1. Sectionformat {Radon Families}{1}
3.2. Sectionformat {$pi $-systems}{1}
3.3. Sectionformat {Complex Radon Measures}{1}
3.4. Sectionformat {The Fell Topology on the Space of Subgroups}{1}
3.5. Sectionformat {Borel Hilbert Bundles}{1}
3.6. Sectionformat {The Hilbert Space $L^2(X,H )$}{1}
3.7. Sectionformat {The Hilbert Space $ltpguh $}{1}
3.8. Sectionformat {The Quotient Borel Structure}{1}
Chapter 4. Proof of the Equivalence Theorem
4.1. Sectionformat {The cs -Algebra of the Linking Groupoid}{1}
4.2. Sectionformat {Approximate Units}{1}
Chapter 5. Basic Representation Theory
5.1. Sectionformat {Invariant Ideals}{1}
5.2. Sectionformat {The Support of a Representation}{1}
5.3. Sectionformat {Inducing Representations}{1}
5.4. Sectionformat {Supports of Induced Representations}{1}
5.5. Sectionformat {Irreducible Representations}{1}
5.6. Sectionformat {cs -Bundles}{1}
5.7. Sectionformat {Type Structure}{1}
5.8. Sectionformat {Closed Orbits}{1}
5.9. Sectionformat {Inducing Irreducible Representations}{1}
5.10. Sectionformat {The Non-Smooth Case}{1}
Chapter 6. The Existence and Uniqueness of Haar Systems
6.1. Sectionformat {First Steps}{1}
6.2. Sectionformat {Group Bundles}{1}
6.3. Sectionformat {The Isotropy Groupoid and the Isotropy Map}{1}
6.4. Sectionformat {Haar Systems on 'Etale Groupoids}{1}
6.5. Sectionformat {Haar Systems on Equivalent Groupoids}{1}
6.6. Sectionformat {Some Applications}{1}
Chapter 7. Unitary Representations
7.1. Sectionformat {Quasi-invariant Measures}{1}
7.2. Sectionformat {Unitary Representations}{1}
7.3. Sectionformat {An Example: Regular Representations}{1}
Chapter 8. Renault's Disintegration Theorem
8.1. Sectionformat {The Statement}{1}
8.2. Sectionformat {The Proof}{1}
Chapter 9. Amenability for Groupoids
9.1. Sectionformat {Some Comments on the Group Case}{1}
9.2. Sectionformat {First Definitions}{1}
9.3. Sectionformat {Amenable Groupoids}{1}
9.4. Sectionformat {Amenable Maps}{1}
9.5. Sectionformat {Amenability and Equivalence}{1}
9.6. Sectionformat {Topological Invariant Means}{1}
9.7. Sectionformat {Borel Equivalence}{1}
9.8. Sectionformat {Applications and Examples}{1}
Chapter 10. Measurewise Amenability for Groupoids
10.1. Sectionformat {Means}{1}
10.2. Sectionformat {Measurewise Invariant Means}{1}
10.3. Sectionformat {Fun with Means}{1}
10.4. Sectionformat {Measurewise Amenability and Equivalence}{1}
10.5. Sectionformat {Amenable Measures}{1}
10.6. Sectionformat {An Application}{1}
Chapter 11. Comments on Simplicity
11.1. Sectionformat {The Auxillary Groupoids}{1}
11.2. Sectionformat {Restricting to the Isotropy}{1}
11.3. Sectionformat {Renault's Simplicity Result}{1}
11.4. Sectionformat {The Amenable Case}{1}
Appendix A. Duals and Topological Vector Spaces
A.1. Sectionformat {The Strict Dual}{1}
A.2. Sectionformat {Projective Tensor Products}{1}
A.3. Sectionformat {The Dual of $coxlone $}{1}
A.4. Sectionformat {The Dual of $liytlox $}{1}
A.5. Sectionformat {A Dense Subspace of $E ^{**}$}{1}
A.6. Sectionformat {An Alternative Topology}{1}
Appendix B. Remarks on Blanchard's Theorem
Appendix C. The Inductive Limit Topology
Appendix D. Ramsay Almost Everywhere
Answers to Some of the Exercises
Bibliography
Notation and Symbol Index
Index