Differential Topology

For doctoral students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University

Syllabus

Textbooks

• M. Audin and M. Damian, “Morse Theory and Floer Homology”, Springer

Course contents

1. The Arzelà–Ascoli theorem
2. Fredholm theory
3. Distribution spaces and weak solutions
4. Sobolev spaces on $\mathbb{R}^n$
5. The Cauchy–Riemann equation
6. The Banach manifold $\mathcal{P}^{1,p}(x,y)$