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Title page

Chapter 1. Introduction

Chapter 2. Preliminary

2.1. Notation

2.2. Actions and cocycle actions

2.3. Core and canonical extension

2.4. Ultraproduct von Neumann algebras

2.5. Ultraproduct of reduced von Neumann algebras

Chapter 3. Flows on ultraproduct von Neumann algebras

3.1. \om-equicontinuity

3.2. (\al,\om)-equicontinuity

3.3. Flows on \cM_{\al}^{\om} or \cM_{\om,\al}

3.4. Connes spectrum of \al_{\om}

3.5. Lift of Borel unitary path

Chapter 4. Rohlin flows

4.1. Rohlin flows

4.2. Invariant approximate innerness

Chapter 5. Classification of Rohlin flows

5.1. Rohlin projection and averaging technique

5.2. 2-cohomology vanishing

5.3. Approximation by cocycle perturbation

5.4. Approximate vanishing of 1-cohomology

5.5. Proof of the main theorem

Chapter 6. Applications

6.1. Classification of invariantly approximately inner flows

6.2. Examples of Rohlin flows on the injective factor of type II₁

6.3. The classification of injective factors of type III

6.4. Non-fullness of type III₀ factors

6.5. Product type flows \index{product type flow}

6.6. Quasi-free flows on Cuntz algebras

Chapter 7. Characterization of Rohlin property

Chapter 8. Concluding remarks and Problems

Chapter 9. Appendix

9.1. Basic measure theoretic results

9.2. Kac algebraic proof of the 2-cohomology vanishing

9.3. Approximation by using continuous unitary path

9.4. Borel cocycle actions

9.5. Unitary representations and 1-cocycles

9.6. Disintegration of automorphisms

Bibliography

Index

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