I.Contents:
Differentiable manifolds, vector bundles, Connections, spin structure, Laplace and Dirac operators, De Rham cohomology, Hodge theory, Morse theory, Floer homology
II.Course prerequisite:
undergraduate geometry
undergraduate algebra
undergraduate analysis
III.Reference material ( textbook(s) ):
J邦rgen Jost, Riemannian geometry and geometric analysis 3rd ed, Chapters 1,2,3,6,7
IV.Grading scheme:
Homework: 40%
Midterm Exam: 30%
Final Exam: 30%
V.Others: