MAT8021 - Algebraic Topology, Spring 2021

• Here is the exam.

• The final exam will take place on Friday, June 11, 4:30-6:30 pm, in Teaching Building 1, Room 502.

• Office hours during the final exam weeks: Thursday, June 3, Monday, June 7, 10:00-11:30 am; Thursday, June 10, 2:30-4:00 pm.

• Assignment 13 required, not collected

• Assignment 12 due Tuesday, May 18

• Assignment 11 due Friday, May 7

• The cohomology ring of a lens space

• Assignment 10 due Tuesday, Apr. 27

• Assignment 9 due Tuesday, Apr. 20

• Assignment 8 due Tuesday, Apr. 13

• Assignment 7 due Tuesday, Apr. 6

• Lecture 9, Mar. 26, a correction

• Assignment 6 due Tuesday, Mar. 30

• Assignment 5 due Tuesday, Mar. 23

• Assignment 4 due Tuesday, Mar. 16

• Assignment 3 due Tuesday, Mar. 9

• Assignment 2 due Tuesday, Mar. 2 (corrected problem 4, Jan. 25)

• As the lectures progress, to solidify your understanding as well as appreciate the subject, you are strongly recommended to work through the relevant portion of Hatcher's book. Even better, reading from different sources, both printed and online, is helpful for acquiring perspectives. The winter break can potentially be a good opportunity for you to get into this.

• Assignment 1 due Tuesday, Jan. 19

Instructor

朱一飞 ZHU Yifei

Huiyuan 3-419

8801 5911

zhuyf@sustech.edu.cn

Office Hours: Monday 2:30-4:00 pm, Thursday 10:00-11:30 am

Grader: 梁桐桐 LIANG Tongtong

Class QQ group: 926793849

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 homology and cohomology.

For undergraduate students, this is a sequel to MA323 Topology, developing further algebraic (and computable) machinery beyond the fundamental group and covering maps to analyze spaces qualitatively.

Prerequisites

Topology (MA323) or consent of the department.

Textbooks

The main references will be Hatcher's Algebraic Topology (online version available here along with additional exercises and content items) and 姜伯驹《同调论》.

This semester we will cover homology and cohomology roughly corresponding to Chapters 2 and 3 of Hatcher, along with supplementary materials such as fiber bundles, characteristic classes, and spectral sequences. Jiang's Chinese text is also quite handy and helpful at times.

Exams

There will be one final exam worth 50% of your final grade.

Homework

The assigned problems for each week are due each Tuesday in-class at 2 pm, 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.