Course title
6M0177001
Cohomology of classifying spaces
Course content
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.
Purpose of class
The purpose of this course is to provide materials for writing a master's thesis in algebraic topology.
Goals and objectives
1. Can explain classifying spaces.
2. Can explain spectral sequences.
3. Can compute cohomology using spectral sequences.
Language
English
Class schedule

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
Prerequisites
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.
Regionally-oriented
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
Active-learning course
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