Geometry IIA

Term 3, 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

Course contents

1. Definition of manifolds
2. Examples of manifolds
3. $C^{\infty}$ functions
4. $C^{\infty}$ maps; directional derivatives
5. Tangent spaces
6. Differentials of $C^{\infty}$ maps
7. Examples of differentials of $C^{\infty}$ maps; local properties of maps, part 1
8. Local properties of maps, part 2; projective spaces