講義名 幾何学特論E1（Advanced topics in Geometry E1） 科目コード：MTH.B505
開講学期 １Q 単位数 1--0--0
担当 五味 清紀 教授：本館２階２２２号室（内線２２１９）
【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. This lecture start with an exposition the definition and basic properties of vector bundles, and then introduces topological K-theory.
【到達目標】
to understand basic properties of vector bundles.
to understand a definition of topological K-theory.
【キーワード】
vector bundles, K-theory
【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 definition and examples of vector bundles |
| Class 2 | Basic properties of vector bundles |
| Class 3 | Subbundle and quotient bundle |
| Class 4 | Vector bundles on compact Hausdorff spaces, I |
| Class 5 | Vector bundles on compact Hausdorff spaces, II |
| Class 6 | A definition of K-theory |
| Class 7 | Product in K-theory |
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.B203 ： Introduction to Topology III
MTH.B204 ： Introduction to Topology IV
MTH.B341 ： Topology
【履修の条件（知識・技能・履修科目等）】
require proficiency in basic topology and algebra.