Spinors on Singular Spaces and the Topology of Causal Fermion Systems.

Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Basic Definitions and Simple Examples -- Chapter 3. Topological Structures -- 3.1. A Sheaf -- 3.2. A Topological Vector Bundle -- 3.3. A Bundle over a Topological Manifold -- 3.4. A Bundle over a Differentiable Manifold -- Chapter 4. Topological Spinor Bundles -- 4.1. Clifford Sections -- 4.2. Topological Obstructions -- 4.3. The Spin Group -- 4.4. Construction of Bundle Charts -- 4.5. Spin Structures -- Chapter 5. Further Examples -- 5.1. Compact Riemannian Spin Manifolds -- 5.2. Almost-Complex Structures on Riemannian Manifolds -- 5.3. Complex Structures on Riemannian Manifolds -- 5.4. Kähler Structures -- Chapter 6. Tangent Cone Measures and the Tangential Clifford Section -- 6.1. The Tangent Cone Measure -- 6.2. Construction of a Tangential Clifford Section -- 6.3. Construction of a Spin Structure -- Chapter 7. The Topology of Discrete and Singular Fermion Systems -- Chapter 8. Basic Examples -- 8.1. The Euclidean Plane -- 8.2. Two-Dimensional Minkowski Space -- 8.3. The Euclidean Plane with Chiral Asymmetry -- 8.4. The Spin Structure of the Euclidean Plane with Chiral Asymmetry -- 8.5. The Spin Structure of Two-Dimensional Minkowski Space -- Chapter 9. Spinors on Singular Spaces -- 9.1. Singularities of the Conformal Factor -- 9.2. Genuine Singularities of the Curvature Tensor -- 9.3. The Curvature Singularity of Schwarzschild Space-Time -- 9.4. A Lattice System with Non-Trivial Topology -- Acknowledgments -- Bibliography -- Back Cover.

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.