Differential Geometry and Topology in Physics, Spring 2019
lecture1 (Euler characteristics and supersymmetric quantum mechanics)
lecture2 (manifolds, tangent spaces)
lecture3 (vector fields, tangent bundles, orientation)
lecture4 (cotangent bundles, differential forms)
lecture5 (de Rham cohomology, metric, harmonic forms, Hodge theorem, Poincare duality)
lecture6 (Riemannian geometry, Gauss-Bonnet theorem, Einstein equations)
lecture7 (simplicial homology groups, homotopy)
lecture8 (cohomology groups, Lefschetz fixed-point theorem, Poincare-Hopf theorem)
lecture9 (fundamental groups, homotopy groups)
lecture10 (Lie groups, Lie algebras, vector bundles)
lecture11 (principal G-bundles, connections, curvatures, Yang-Mills action)
lecture12 (characteristic classes, Chern-Weil theory)
lecture13 (index theorem, Hirzebruch-Riemann-Roch theorem, anomaly, supersymmetry)
I have taught the same course in 2017. But I have updated the lecture note by making corrections and adding more contents.
Lecture notes are written by referring to various sources without mentioning it. Comments are welcome.