2021 Advanced topics in Geometry A1

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Gomi Kiyonori 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Fri5-6()  
Group
-
Course number
MTH.B405
Credits
1
Academic year
2021
Offered quarter
1Q
Syllabus updated
2021/4/26
Lecture notes updated
-
Language used
English
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Course description and aims

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.

Student learning outcomes

-to understand basic properties of vector bundles.
-to understand a definition of topological K-theory.

Keywords

vector bundles, topological K-theory

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

A standard lecture course.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The definition and examples of vector bundles Details will be provided during each class session
Class 2 Basic properties of vector bundles Details will be provided during each class session
Class 3 Subbundle and quotient bundle Details will be provided during each class session
Class 4 Vector bundles on compact Hausdorff spaces, I Details will be provided during each class session
Class 5 Vector bundles on compact Hausdorff spaces, II Details will be provided during each class session
Class 6 A definition of K-theory Details will be provided during each class session
Class 7 Product in K-theorys Details will be provided during each class session

Out-of-Class Study Time (Preparation and Review)

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.

Textbook(s)

No textbook is set.
Lecture note will be provided.

Reference books, course materials, etc.

M. F. Atiyah, K-theory. Lecture notes by D. W. Anderson W. A. Benjamin, Inc., New York-Amsterdam 1967

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.B203 : Introduction to Topology III
  • MTH.B204 : Introduction to Topology IV
  • MTH.B341 : Topology
  • LAS.M106 : Linear Algebra II
  • MTH.A201 : Introduction to Algebra I
  • MTH.A202 : Introduction to Algebra II
  • MTH.A203 : Introduction to Algebra III
  • MTH.A204 : Introduction to Algebra IV

Prerequisites (i.e., required knowledge, skills, courses, etc.)

require proficiency in basic topology (MTH.B203, MTH.B204, MTH.B341) and algebra (LAS.M106, MTH.A201, MTH.A202, MTH.A203, MTH.A204)

Other

Use T2SCHOLA.

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