lecture 01: Goals, big picture
lecture 02: The 2d toric code
lecture 03: The toric code as a gauge theory, phase diagram
lecture 04: Definition of homology, Z_N p-form toric code
lecture 05: Homology of cell complexes, examples; dependence on the gauge group; long exact sequences
lecture 06: Subdivision invariance of homology from entanglement renormalization; gapped boundaries and relative homology
lecture 07: Duality - Poincare and otherwise
lecture 08: Supersymmetric quantum mechanics
lecture 09: Supersymmetry and cohomology; non-linear sigma model
lecture 10: de Rham cohomology
lecture 11: Morse theory
lecture 12: Tunneling in supersymmetric quantum mechanics; pullback; Mayer-Vietoris sequence
lecture 13: Many different things that are called Poincare duality; Cech cohomology
lecture 14: Cech cohomology and the toric code; Cech cohomology with real coefficients is de Rham cohomology
lecture 15: Homotopy invariance of (co)homology; Homotopy invariance and Morse theory; Homotopy groups
lecture 16: Basic properties of homotopy groups; van Kampen theorem; fundamental group of a cell complex
lecture 17: The quantum double model
lecture 18: Vector bundles and connections; the Dirac monopole and the Hopf bundle
lecture 19: A little bit of Chern classes and homotopy groups of Lie groups; quantum double groundstates and the fundamental group
lecture 20: Chern-Simons theory and knot invariants