Bugarin, Enrico Paolo: On quotient cohomology of substitution tiling spaces. 2014
Inhalt
- Introduction
- Chapter 1. Preliminaries
- 1.1. Direct limits
- 1.2. CW complexes
- 1.3. Cech cohomology of CW complexes
- 1.4. Inverse limit spaces and their cohomology
- 1.5. Perron-Frobenius theory
- 1.6. Symbolic substitution
- Chapter 2. Substitution tiling spaces and their cohomology
- 2.1. Substitution tilings and tiling spaces
- 2.2. Equivalence of tiling spaces
- 2.3. Tiling spaces are inverse limit spaces
- 2.4. The Cech cohomology of tiling spaces
- 2.5. Dynamical zeta functions
- Chapter 3. Quotient cohomology between tiling spaces
- Chapter 4. One-dimensional substitution tiling spaces
- 4.1. The twisted Fibonacci substitution
- 4.2. The universal morphism
- 4.3. Generalised Thue-Morse and period doubling substitutions
- Chapter 5. Two-dimensional substitution tiling spaces
- 5.1. The squiral tiling and its factors
- 5.2. The Chacon tiling space and its factors
- 5.3. The generalised chair tilings
- Outlook
- Bibliography