vi CONTENTS 5.5. Gap labeling and K-theory 67 5.6. Averages and Ruelle-Sullivan currents 68 5.7. PE cohomology and rotations 70 Chapter 6. Tricks of the trade 75 6.1. One dimensional methods 75 6.2. Partial collaring 78 6.3. Relative cohomology and eventual ranges 80 6.4. Barge-Diamond collaring 83 6.5. The pinwheel tiling 90 Chapter 7. Relaxing the rules II: Tilings without finite local complexity 95 7.1. Fault lines 95 7.2. Analyzing a fault line — 1 dimensional dynamics 98 7.3. A simple 2-dimensional example 99 7.4. The local topology of ΩΣ 101 7.5. Inverse limit structures 102 7.6. A more involved example 104 7.7. Conclusions 107 Appendix A. Solutions to selected exercises 109 Bibliography 117
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