2021 Advanced courses in Geometry B

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Academic unit or major
Mathematics
Instructor(s)
Gomi Kiyonori 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Fri5-6(H117)  
Group
-
Course number
ZUA.B332
Credits
1
Academic year
2021
Offered quarter
2Q
Syllabus updated
2021/3/19
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. 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.

Student learning outcomes

-to understand basic properties of topological K-theory.
-to understand an application of topological K-theory.

Keywords

vector bundles, K-theory, Bott periodicity, Thom isomorphism

Competencies that will be developed

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

Class flow

This is a standard lecture course.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The homotopy axiom and the excision axiom Details will be provided during each class session
Class 2 The exactness axiom Details will be provided during each class session
Class 3 The Bott periodicity, I Details will be provided during each class session
Class 4 The Bott periodicity, II Details will be provided during each class session
Class 5 The Thom isomorphism theorem, I Details will be provided during each class session
Class 6 The Thom isomorphism theorem, II Details will be provided during each class session
Class 7 Application 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)

non required

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)

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