幾何学 II / 幾何学概論 II
The course gives an introduction to algebraic topology through the
theory of differential forms and de Rham cohomology groups. Among
other things, we will prove the Brouwer fixed point theorem and the
invariance of domain. Lectures are given in Japanese.
Here is a more detailed syllabus in Japanese:
Text: Ib Madsen and Jørgen Tornehave: From Calculus to
Cohomology: De Rham Cohomology and Characteristic Classes,
Cambridge University Press, 1997.
Lecture notes: The Lecture Notes are
updated as necessary.
Time and place: Tuesday 10:30-12:00 in Science Building 1, Room 109.
Schedule: Here is a preliminary course schedule:
- Lecture 1: Introduction.
- Lecture 2: The alternating algebra.
- Lecture 3: The alternating algebra, continued.
- Lecture 4: Differential forms.
- Lecture 5: de Rham cohomology.
- Lecture 6: The Poincare lemma.
- Lecture 7: Cochain complexes and their cohomology.
- Lecture 8: Partition of unity.
- Lecture 9: The Mayer-Vietoris sequence.
- Lecture 10: Homotopy invariance.
- Lecture 11: Homotopy invariance, continued.
- Lecture 12: Brouwer's theorems.
- Lecture 13: The Jordan-Brouwer separation theorem.
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