Theme: Introduction to Topology Students will learn the fundamentals of topology, especially homology groups and fundamental groups, and understand how to use them to classify topological spaces. If possible, the course will also touch on topics related to knot theory and three- or four-dimensional topology. It also enhances the development of students' skill in making oral presentation and self-regulated learning.
The goals of this course are to - recognize the basic concepts of homology groups and fundamental groups, - be able to classify topological spaces using them, - be able to explain simple examples of the classifications.
授業の内容や構成 Course Content / Plan
選んだ教科書を中心に関連する参考書も参照して，トポロジーの基礎を学ぶ．毎週1，2コマ程度，各自が学んだことを交替で発表する． Students should refer to the chosen textbook and several articles to study the basic topology. They should give talks on their own understanding in rotation, in 1 or 2 periods a week.
履修条件 Course Prerequisites
定員超過の場合の選考方法: 希望提出前に担当教員に連絡をとった学生を優先する． The students contacting the instructor before application will have priority.
関連する科目 Related Courses
幾何学続論． Advanced Course of Geometry.
成績評価の方法と基準 Course Evaluation Method and Criteria
セミナーでの出席と発表の状況で判断する．ホモロジー群や基本群についての基本的な概念を理解し，それらを用いた位相空間の簡単な分類の例を説明できることを合格の基準とする． Grading will be based on attendance and oral presentation in the seminar. To pass, students must - recognize the basic concepts of homology groups and fundamental groups, - be able to explain simple examples of the classifications topological spaces using them.
不可(F)と欠席(W)の基準 Criteria for “Fail(F)” & “Absent(W)” grades
全く出なくなれば，欠席扱いになります．
教科書・テキスト Textbook
下記または他の文献から選ぶ． Will be chosen among the following book or other advanced articles. * 加藤十吉「位相幾何学」(裳華房)
参考書 Reference Book
セミナー中に紹介する． Will be introduced in the seminar.
課外学習等 (授業時間外学習の指示) Study Load(Self-directed Learning Outside Course Hours)
十分な予習に時間もかかることに注意．Students will take a lot of time to prepare for them sufficiently. 宿題は授業時間外に解くこと．Homework assignments to be completed outside of class hours.
