2020 Advanced topics in Geometry B

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Gomi Kiyonori 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Tue3-4(H104)  
Group
-
Course number
MTH.B402
Credits
1
Academic year
2020
Offered quarter
2Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

The most basic characteristic classes of vector bundles are introduced. Their basic properties and applications are also explained.

Student learning outcomes

- to understand a definition and properties of the most basic characteristic classes of vector bundles.
- to learn applications of these characterisitic classes.

Keywords

vector bundle, Euler class, Stiefel-Whiteny class, Chern class, Pontryagin class, index theorem, exotic sphere

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 Thom class and Euler class Details will be provided during each class session
Class 2 Applications of Euler class Details will be provided during each class session
Class 3 Stiefel-Whiteny class Details will be provided during each class session
Class 4 Chern class Details will be provided during each class session
Class 5 Pontryagin class Details will be provided during each class session
Class 6 Index theorem Details will be provided during each class session
Class 7 Exiotic sphere 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.

John Milnor, James D. Stasheff, Characteristic Classes. Volume 76 (Annals of Mathematics Studies), Princeton University Press.
Ichiro Tamura, Differential Topology, Iwanami.

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.B341 : Topology
  • MTH.B301 : Geometry I
  • MTH.B302 : Geometry II
  • MTH.B401 : Advanced topics in Geometry A
  • ZUA.B331 : Advanced courses in Geometry A

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

Knowledge on topology (MTH.B341) and maniofolds (MTH.B301, MTH.B302) are required. Also, students are supposed to have attended Advanced topics in Geometry A(MTH.B401) or Advanced courses in Geometry A(ZUA.B331).

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