Topology and Condensed Matter Physics

Chapter 1. Overview of Topological Ideas in Condensed Matter Physics.- Chapter 2. Set Topology.- Chapter 3. Homotopy theory.- Chapter 4. Homology.- Chapter 5. Differential Topology and Differential Geometry.- Chapter 6. Vector Bundles.- Chapter 7. Special Topics: A Crash Course on Knots.- Chapter 8. Special Topics: A Short Course on Group Theory.- Chapter 9. Use of Topology in physical problems.- Chapter 10. What is dimension?.- Chapter 11. Quantum Geometry and Topology.- Chapter 12. Topology, geometry and quantum interference in condensed matter physics.- Chapter 13. Dirac quasiparticles and Majorana modes in condensed matter systems.- Chapter 14. Vertex Models and Knot invariants.- Chapter 15. Concepts of polymer statistical topology.- Chapter 16. Introduction to abelian and non-abelian anyons.-Chapter 17. An introduction to Quantum Spin Liquids.- Chapter 18. Topological aspects of quantum information processing.

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• Física da Matéria Condensada (física do estado sólido e estado líquido)
• Modelação matemática
• Topologia
• Física Matemática

Topological Ideas;Condensed Matter;Set Topology;Homotopy theory;Homology;Differential Topology;Vector Bundles;Quantum Geometry;Abelian Groups;The Knot Group