MA3F1 Introduction to topology
Term I 2024-2025

Module Description

In this module, MA3F1 (Introduction to topology) we assume as background the material from MA260 (Norms, metrics, and topologies) or from MA222 (Metric spaces), and from MA136 (Introduction to abstract algebra).

Topology is the study of shapes: topological spaces without any notion of geometry. We begin by saying precisely what it means for two spaces \(X\) and \(Y\) to be "the same" in the topological setting. This done we investigate one of the most powerful topological invariants: the fundamental group \(\pi_1(X)\). The justly named fundamental group is also directly related to covering spaces which we will cover in detail.

The material covered in this module is directly relevant to MA3H5 (Manifolds), MA3H6 (Algebraic topology), and many other modules.

Schedule

The schedule has a planned list of topics, organized by lecture. We will change the schedule as necessary, as we work through the material. Links to (handwritten) lecture notes and example sheets will be posted week-by-week (or perhaps a bit faster...). Recorded lectures are available via lecture capture.

Instructor and TAs

Name Building/Office E-mail Phone Office Hours
Saul Schleimer B2.14 Zeeman s dot schleimer at warwick dot ac dot uk 024 7652 3560 Tuesday 12noon
Layne Hall NA layne.hall@warwick.ac.uk NA NA

Class meetings

Activity Led by Time Room
Lecture Schleimer Monday 10:00-11:00 MS.03
Support class Hall Monday 16:00-17:00 L5
Lecture Schleimer Tuesday 11:00-12:00 L5
Lecture Schleimer Thursday 11:00-12:00 MS.03
Support class Hall Thursday 18:00-19:00 MS.05

Reference materials

There are two typeset versions of the lecture notes, due to Lotz in 2019 and Sparrow and Smillie in 2020 and 2023. These should track the content covered in our lectures somewhat.

Note, however, that those notes, and our lectures, will very closely follow a subset of chapters zero and one of the book Algebraic topology, by Allen Hatcher. A PDF copy is freely available from Hatcher's website. A physical copy can be purchased on-line and from certain bookstores.

Links to lecture capture and the discussion forum are on the module's Moodle page.

Example sheets

See the schedule for the example sheets.

In addition to the exercises in the example sheets, Hatcher's book contains many interesting exercises. He has also given additional exercises.

Exam

The exam will be 85% of your mark. The exam will be closed book. Here are the exam papers for this module from the last five years.

Assessed work

Assessed work will be 15% of your mark. Of this, 5% may be earned in weeks 3, 5, 7, and 9 by submitting the indicated exercise to the Moodle page. This will be marked by the TA with a score of 0, 1, 2, 3, 4, or 5. Please let me (Saul) know if any of the problems are unclear or have typos. I will post model solutions to selected problems weekly.

Assessed work is due Friday at 12noon in weeks 3, 5, 7, and 9.

You must record your name, the date, the assignment number, and the module code (MA3F1) at the top of your completed work. If you collaborate with other students, you must include their names.

Solutions typeset using LaTeX are strongly preferred. If your solution is not readable you will lose marks. You must check the spelling and grammar of your work before turning it in. If you do not properly edit your work you will lose marks.

Mistakes

Please tell me in person, or via email, about any errors on this website or made in class. I am especially keen to hear about mathematical errors, gaffes, or typos made in lecture or in the example sheets.