幾何学特論F1

【講義の概要とねらい】
Topological K-theory is one of the generalized cohomology theories, and roughly classifies vector bundles over topological spaces. In this lecture, the basic properties of topological K-theory including the Bott periodicity and the Thom isomorphism theorem will be explained. An application will also be provided at the end of the lecture.

【到達目標】
to understand basic properties of topological K-theory.
to understand an application of topological K-theory.

【キーワード】
vector bundles, K-theory, Bott periodicity, Thom isomorphism

【学生が身につける力】
Specialist skills

【授業の進め方】
A standard lecture course.

【授業計画・課題】

Class 1	The homotopy axiom and the excision axiom
Class 2	The exactness axiom
Class 3	The Bott periodicity, I
Class 4	The Bott periodicity, II
Class 5	The Thom isomorphism theorem, I
Class 6	The Thom isomorphism theorem, II
Class71	Application

Details will be provided during each class session.

【授業時間外学修（予習・復習等）】
Formal Message: To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

【教科書】
No textbook is set. Lecture note will be provided.

【参考書、講義資料等】
M. F. Atiyah, K-theory. Lecture notes by D. W. Anderson W. A. Benjamin, Inc., New York-Amsterdam 1967

【成績評価の基準及び方法】
Assignments (100%).

【関連する科目】
MTH.B505 ： Advanced topics in Geometry E1

【履修の条件（知識・技能・履修科目等）】
proficiency in basic topology and algebra