6M017700
1 Cohomology of classifying spaces
Classifying spaces are objects of study in algebraic topology. In this course, we learn spectral sequences that are tools
in computation of the cohomology of classifying spaces.
The purpose of this course is to provide materials for writing a master's thesis in algebraic topology.
- Can explain classifying spaces.
- Can explain spectral sequences.
- Can compute cohomology using spectral sequences.
|
Class schedule |
HW assignments (Including preparation and review of the class.) |
Amount of Time Required |
1. |
Classifying Space |
Handouts |
200minutes |
2. |
Spectral Sequence |
Handouts |
200minutes |
3. |
The Leray-Hirsh Theorem |
Handouts |
200minutes |
4. |
Gysin Sequence |
Handouts |
200minutes |
5. |
Eilenberg-MacLane Space |
Handouts |
200minutes |
6. |
The Transgression Theorem |
Handouts |
200minutes |
7. |
Review |
Handouts |
200minutes |
8. |
NA |
NA |
0minutes |
9. |
NA |
NA |
0minutes |
10. |
NA |
NA |
0minutes |
11. |
NA |
NA |
0minutes |
12. |
NA |
NA |
0minutes |
13. |
NA |
NA |
0minutes |
14. |
NA |
NA |
0minutes |
Total. |
- |
- |
1400minutes |
Relationship between 'Goals and Objectives' and 'Course Outcomes'
|
Report |
Total. |
1. |
10% |
10% |
2. |
20% |
20% |
3. |
70% |
70% |
Total. |
100% |
- |
Evaluation method and criteria
Report 100%. You will receive a passing grade if you understand the explanations given in the class and clearly state the
reasoning in your report.
Textbooks and reference materials
Allen Hatcher, Algebraic topology, Cambridge University Press, 2002. http://pi.math.cornell.edu/~hatcher/AT/ATpage.html
Peter May, A Concise Course in Algebraic Topology, University of Chicago Press, 1999. http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
Abstract algebra (group theory, linear algebra over finite fields), Point set topology, Category theory.
Office hours and How to contact professors for questions
- Friday 9:00--10:40
- Send me e-mail.
Non-regionally-oriented course
Development of social and professional independence
- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
More than one class is interactive
Course by professor with work experience
Work experience |
Work experience and relevance to the course content if applicable |
N/A |
該当しない |
Education related SDGs:the Sustainable Development Goals
- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sun Mar 21 16:13:28 JST 2021