Notes

1. Notes of Xiaobo Liu's symplectic geometry course

The course covered the basic materials of symplectic geometry and gave a friendly introduction to the Gromov-Witten invariants.

And here is some remarks about the course (Update: 2024.6.6)

2. Basics of 3-manifolds

This is a hand-written notes when I read Martelli's beautiful book.

3. Basics of Kirby calculus

This is a hand-written notes when I read 4-Manifolds And Kirby Calculus.

4. Exotic 4-manifolds

This is a hand-written notes of Lisa Piccirillo's wonderful mini-course.

5. Introduction to gauge theory (In progress)

This is a tex-written notes of gauge theory. I try to cover Seiberg-Witten theory, Yang-Mills theory and Heegaard Floer theory. But I have only written some basics of SW invariants, so....🫣

6. BS thesis (in chinese): On the classification of symplectic 4-manifolds with PSC metric 

This is my BS thesis, which contains two parts,

• McDuff's rational or ruled theorem: If a symplectic 4-manifold contains a symplectic sphere with non-negative self intersection numbers, then it must be rational or ruled.

• Using Seiberg-Witten theory, one can prove if a symplectic 4-manifold admits a PSC metric, then it will contain a symplectic sphere with non-negative self intersection numbers.

Remark: If you open some links and find Baidu pan wants a code to open it, then ZK03 will work.