Spring 2021 - MATH 841 G100

Topology: Selected Topics (4)

Class Number: 3915

Delivery Method: Remote


  • Course Times + Location:

    Jan 11 – Apr 16, 2021: Tue, Thu, 10:30 a.m.–12:20 p.m.





This is a basic level graduate course with introduction to algebraic topology and its applications in combinatorics, graph theory and geometry.  The course will cover introductory chapters from [1] and parts of [2].  Time permitting, we may touch some recent topics like the topology of random simplicial complexes.  The instructor expects that students with interests in topology and those with interests in discrete mathematics and geometry would find the course suitable.

Course Syllabus

This is a basic level graduate course with introduction to algebraic topology and its applications in combinatorics, graph theory and geometry.  The course will start with a brief review of the basic notions of topology, including the notions mentioned as prerequisites.  It will continue with introductory chapters from Hatcher's textbook [1]. Simplicial complex. Cell complex. Homotopy and fundamental group (Sections 1.1-1.3 and 1.A). Homology (Sections 2.1-2.2 and parts of 2.A-2.C).

The second part of the course will concentrate on various applications of algebraic topology in combinatorics, graph theory, and geometry. We will follow relevant chapters from Matou\v{s}ek's book [2]. Some of those applications use Borsuk-Ulam Theorem, which will be covered first.

Time permitting, we may touch a recent flourishing topics on the topology of random simplicial complexes.

The instructor expects that students with interests in topology and those with interests in discrete mathematics and geometry will find the course suitable.

This course will be delivered online.
You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.


  • Homework 20%
  • Midterm 30%
  • Final Exam 50%


Instruction Details

The weekly schedule will consist of four 50-minute lectures. Two to three of them will be giving new material, with some details left for the students to cover by themselves from the provided textbooks. The remaining weekly time will be used for tutorials, covering problems and examples, explaining details of proofs, and having students work in small groups and report on their solutions.

The online platform used will be Zoom, with synchronous teaching that will be recorded for asynchronous viewing.

Additional comments

The course will be offered through the PIMS network of universities in Western Canada and the instructor reserves the right to limit the number of students from outside of SFU.  He will allow auditing for additional students who will not take the course for credit (their homework and exams will not be graded).

Instructor reserves the right to make modifications to the outline.


Course Prerequisites

Topological space, continuous maps, metric space topology, quotient topology, compactness.  Basic notions about simplicial complexes, fundamental groups and covering spaces will be helpful, but students will also be given opportunity to self-study about these notions during the first month of the course and help will be offered during tutorials.



[1] A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. Available for free download from http://pi.math.cornell.edu/~hatcher/AT/ATpage.html

[2] J. Matousek, Using the Borsuk–Ulam Theorem - Lectures on Topological Methods in Combinatorics and Geometry, Springer, 2003.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:


SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html


Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).