2020 Advanced courses in Geometry A

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Academic unit or major
Mathematics
Instructor(s)
Gomi Kiyonori 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue3-4(H104)  
Group
-
Course number
ZUA.B331
Credits
1
Academic year
2020
Offered quarter
1Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
English
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Course description and aims

Characteristic classes of vector bundles are invariants which have been applied universally in geometry. Basic properties of cohomology required for the introduction of the characteristic classes, vector bundles and their related notions will be explained.

Student learning outcomes

- to get deeper understanding of cohomology of topological spaces.
- to understand vector bundles and related notions.

Keywords

vector bundle

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 review of homology Details will be provided during each class session
Class 2 review of cohomology Details will be provided during each class session
Class 3 definition of vector bundles Details will be provided during each class session
Class 4 Remannian metric Details will be provided during each class session
Class 5 maps of vector bundles and subbundles Details will be provided during each class session
Class 6 orientation of vector bundle Details will be provided during each class session
Class 7 theorem of Leray-Hirsch 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

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

Knowledge on topology (MTH.B341) and maniofolds (MTH.B301, MTH.B302) are required.

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