Ebook: Quantum topology and global anomalies

This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included. The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level 1. The Ongoing Quest For Three-Manifold Invariants -- 2. Mapping Class Groups and 3-Manifold Invariants -- 3. Teichmuller Spaces and Mapping Class Groups -- 4. Mapping Class Groups and Arithmetic Groups -- 5. Weil-Petersson Geometry of Teichmuller Spaces -- 6. Gauge Theories on Riemann Surfaces I: Bundles -- 7. Gauge Theories on Riemann Surfaces II: Connections -- 8. Geometric Quantization of Chern-Simons-Witten Theories -- 9. Deformation Quantization -- 10. Chiral and Gravitational Anomalies -- 11. Anomalies and the Index Theorem -- 12. Global Anomalies -- 13. Mapping Class Groups and Global Anomalies -- 14. Exotic Spheres