MAT8021 – Algebraic Topology, Spring 2023
• Final exam on Monday, Jun. 12, 10:30 am–12:30 pm in Lecture Hall 1 Room 305: Chapters 5–13.
• Office hours on Thursday, Jun. 8, 10:20 am–12:20 pm or by appointment.
• Ideas and examples of persistent homology begin on page 45 here.
• Assignment 14 required, not collected: Problems 131, 137, 138, 139.
• Assignment 13 due Friday, May 26.
• Assignment 12 due Friday, May 12: Problems 1211, 14, 15, 22.
• Assignment 11 due Friday, May 5: Problems 121, 2, 3, 9.
• Assignment 10 due Friday, Apr. 28.
(Corrected problem 4, Apr. 27)
• Assignment 9 due Friday, Apr. 21: Problems 1112, 14, 15, 16.
• Assignment 8 due Friday, Apr. 14: Problem 114, Exercises 11.2, 11.7 (cf. Example 11.17), 11.9.
• Assignment 7 due Friday, Apr. 7: Problems 102, 106, 107, 108, 1011, 1013, 1014.
• Assignment 6 due Friday, Mar. 31: Exercise 8.7, Problems 81, 82, 83, 85, 86.
• Assignment 5 due Friday, Mar. 24: Problems 73, 75, 712, 713, 714, 718, 719.
• Assignment 4 due Friday, Mar. 17.
• Assignment 3 due Friday, Mar. 10: Exercises 5.31, 5.34, 5.40, Problem 515.
• TOP vs DIFF vs PL
• Assignment 2 due Friday, Mar. 3: Exercise 5.19, Problems 58, 510, 511, 512, 513.
• Assignment 1 due Friday, Feb. 24.
• Motivations for cell complexes, including a nice
article
introducing topological data analysis.
Instructor
朱一飞 ZHU Yifei
College of Science M705
zhuyf@sustech.edu.cn
Office hours: Thursdays 10:20 am–12:20 pm
Grader: 梁嘉诚 LIANG Jiacheng
Objectives
This is a half of the graduate compulsory courses in Geometry and Topology, the other half being MAT8024 Differentiable Manifolds. The main topics
are covering maps and homology.
For undergraduate students, this is a sequel to MA323 Topology, developing further algebraic (and computable) machinery beyond the fundamental group
to analyze spaces qualitatively.
Prerequisites
Topology (MA323) or consent of the department.
Textbooks
We will be working from Chapters 5 to 13 of John M. Lee's
Introduction to topological manifolds, second edition, briefly reviewing compact surfaces and the fundamental group.
Useful references include Allen Hatcher's Algebraic topology,
Haynes Miller's Lectures on
algebraic topology, and 姜伯驹《同调论》.
Exams
There will be one final exam worth 50% of your final grade.
Homework
The assigned problems for each week are due each Friday inclass at 8 am, listed on this page. Homework is worth 50% of your final grade. Students
must make arrangements in advance if they will not be handing in homework on time.
We encourage you to discuss homework problems with your classmates, including strategies for solving different kinds of problems. However, when you
actually write up your solutions, you must do this on your own.
