3. 강의목표
In this course we deal with basic algebraic topology, focusing on homology and cohomology. Topics includes: singular and simplicial homology, homotopy, excision, Mayer-Vieotoris sequence, CW-complexes, applications of homology theory, cohomology, products, universal coefficient and Kunneth theorems, manifolds and Poincare duality.
4. 강의선수/수강필수사항
Undergraduate level 'abstract algebra' and 'point set topology'
5. 성적평가
HW 20%
Mid 35%
Final 45%
6. 강의교재
| 도서명 |
저자명 |
출판사 |
출판년도 |
ISBN |
|
Algebraic topology
|
A. Hatcher
|
Cambridge University Press
|
2002
|
|
7. 참고문헌 및 자료
The lectures will be based, but not entirely, on
- A. Hatcher, Algebraic topology, Cambridge University Press, 2002
This book is available, for free, from the author's website: http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Also, parts of the following books will be often used.
- J. R. Munkres, Elements of algebraic topology, Addison-Wesley, 1984
- J. W. Vick, Homology theory, Academic Press, 1973
- M. J. Greenberg and J. R. Harper, Algebraic topology: a first course, Benjamin-Cummings, 1981
- J. Davis and P. Kirk, Lecture notes in algebraic topology, American Mathematicsl Society, 2001
8. 강의진도계획
We will cover the topics listed above, and the pace will depend on students' performance. Expected schedule is as follows:
Week 1-2 Singular homology, homotopy invariance
Week 3-4 Excision, Mayer-Vieotoris sequence
Week 5-7 CW-complexes, cellular homology, and axioms of homology theory
Week 8 Midterm Exam
Week 9 Some applications of homology theory
Week 10 Singular and cellular cohomology
Week 11-12 Universal coefficient and Kunneth theorems
Week 13-14 Introduction to duality of manifolds
Week 16 Final Exam
9. 수업운영
학교 정책에 따라 비대면 개강 예정이며, 수업을 위한 줌 연결은 아래와 같습니다.
https://us02web.zoom.us/j/85144101920?pwd=U3VJNm5IdW9WZGJkYk5CWm1KVXBYQT09
회의 ID: 851 4410 1920
암호: postech
11. 장애학생에 대한 학습지원 사항
- 수강 관련: 문자 통역(청각), 교과목 보조(발달), 노트필기(전 유형) 등
- 시험 관련: 시험시간 연장(필요시 전 유형), 시험지 확대 복사(시각) 등
- 기타 추가 요청사항 발생 시 장애학생지원센터(279-2434)로 요청