Course title
Topics in Algebraic Topology

kameko masaki
Course content
Starting from reviewing the definition of a group, we recall the group ring. We define the resolution of the integers as a group over a group ring. Then, we define the group cohomology and study some examples including the cyclic group of order 2 and the quaternion group of order 8.
Purpose of class
The purpose of this course is to understand the cohomology of a group through by computing some examples.
Goals and objectives
  1. A successful student will be able to explain the definition of group cohomology.
  2. A successful student will be able to compute the cohomology of a group.
  3. A successful student will be able to discuss some aspects of homological algebra.
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Groups Handouts 200minutes
2. Group rings Handouts 200minutes
3. Resolutions Handouts 200minutes
4. Group cohomology Handouts 200minutes
5. Cohomology of the cyclic group Z/2 Handouts 200minutes
6. Cohomology of the quaternion group Q_8 Handouts 200minutes
7. Final examination Handouts 200minutes
8. - - 0minutes
9. - - 0minutes
10. - - 0minutes
11. - - 0minutes
12. - - 0minutes
13. - - 0minutes
14. - - 0minutes
Total. - - 1400minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Final examination Total.
1. 50% 50%
2. 50% 50%
Total. 100% -
Evaluation method and criteria
Oral examination.
Textbooks and reference materials
Peter May, A Concise Course in Algebraic Topology, Univ. of Chicago Press, 1999. pdf is available in May's webpage.
Kenneth Brown, Cohomology of groups, Springer, 1982.
Undergraduate abstract algebra
Office hours and How to contact professors for questions
  • Friday 9:00--10:40, 1Q, 2020.
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic interpersonal skills
  • Course that cultivates a basic self-management skills
  • 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 applicatable
Education related SDGs:the Sustainable Development Goals
Last modified : Sat Mar 21 14:19:29 JST 2020