Geometry IIB

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

Syllabus

Textbooks

• 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)
2. Y. Matsushima, “多様体入門” (in Japanese), Shokabo

Recommended reading

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

Course contents

1. Immersions and embeddings
2. The embedding theorem; regular and critical points, part 1
3. Regular and critical points, part 2
4. Vector fields, part 1
5. Vector fields, part 2
6. Differential forms, part 1
7. Differential forms, part 2
8. Differential forms, part 3; exam