Topology and Condensed Matter Physics

1. Overview of Topological Ideas in Condensed Matter Physics
Siddhartha Sen

Part I. Topological Tools

2. Set Topology
Somnath Basu, Atreyee Bhattacharya

3. Homotopy theory
Samik Basu, Soma Maity

4. Homology
Dheeraj Kulkarni

5. Differential Topology and Differential Geometry
Kingshook Biswas, Soma Maity

6. Vector Bundles
Utsav Choudhury, Atreyee Bhattacharya

7. Special Topics: A Crash Course on Knots
Mahan Mj

8. Special Topics: A Short Course on Group Theory
Bobby Ezhuthachan

Part II. Physics Problems

9. Use of Topology in physical problems
Somendra M. Bhattacharjee

10. What is dimension?
Somendra M. Bhattacharjee

11. Quantum Geometry and Topology
R. Shankar

12. Topology, geometry and quantum interference in condensed matter physics
Alexander Abanov

13. Dirac quasiparticles and Majorana modes in condensed matter systems
K. Sengupta

14. Vertex Models and Knot invariants
P. Ramadevi

15. Concepts of polymer statistical topology
Sergei Nechaev

16. Introduction to abelian and non-abelian anyons
Sumathi Rao

17. An introduction to Quantum Spin Liquids
Subhro Bhattacharjee

18. Topological aspects of quantum information processing
Ville Lahtinen, Jiannis K. Pachos

Keywords: Mathematics, Mathematical Physics, Mathematical Applications in the Physical Sciences, Condensed Matter Physics