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 13-1, 13-7, 13-8, 13-9.

• Assignment 13 due Friday, May 26.

• Assignment 12 due Friday, May 12: Problems 12-11, 14, 15, 22.

• Assignment 11 due Friday, May 5: Problems 12-1, 2, 3, 9.

• Assignment 10 due Friday, Apr. 28. (Corrected problem 4, Apr. 27)

• Assignment 9 due Friday, Apr. 21: Problems 11-12, 14, 15, 16.

• Assignment 8 due Friday, Apr. 14: Problem 11-4, Exercises 11.2, 11.7 (cf. Example 11.17), 11.9.

• Assignment 7 due Friday, Apr. 7: Problems 10-2, 10-6, 10-7, 10-8, 10-11, 10-13, 10-14.

• Assignment 6 due Friday, Mar. 31: Exercise 8.7, Problems 8-1, 8-2, 8-3, 8-5, 8-6.

• Assignment 5 due Friday, Mar. 24: Problems 7-3, 7-5, 7-12, 7-13, 7-14, 7-18, 7-19.

• Assignment 4 due Friday, Mar. 17.

• Assignment 3 due Friday, Mar. 10: Exercises 5.31, 5.34, 5.40, Problem 5-15.

• TOP vs DIFF vs PL

• Assignment 2 due Friday, Mar. 3: Exercise 5.19, Problems 5-8, 5-10, 5-11, 5-12, 5-13.

• 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 in-class 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.