Geometry IIB

Term 4, Mon. Period 3 · Faculty of Science, Niigata University

Syllabus

Note

This course is held online via Zoom.

Textbooks

1. Y. Matsumoto, “多様体の基礎” (in Japanese), University of Tokyo Press

Main references

1. L. W. Tu, “An Introduction to Manifolds” (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo)

Recommended reading

1. R. Bott and L. W. Tu, “Differential Forms in Algebraic Topology” (Japanese translation by M. Mimura, Maruzen)

Course contents

1. Projective spaces
2. Immersions and embeddings
3. The embedding theorem; partitions of unity
4. Regular and critical points
5. Vector fields, part 1
6. Vector fields, part 2
7. Differential forms, part 1
8. Differential forms, part 2