## MA3F1 Introduction to topology Term I 2017-2018

### Module Description

This module, MA3F1 (Introduction to topology) has the prerequisites MA222 (Metric spaces) and MA249 (Algebra 2).

Topology is the study of shapes: the study of spaces forgetting all notions 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 related, inside topology, to covering spaces and related, for example in number theory, to Galois groups.

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

### 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 example sheets will be posted week-by-week.

### 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 Friday 14:30-15:30
Esmee te Winkel NA e dot te-winkel at warwick dot ac dot uk NA NA
Alessandro Bigazzi NA a dot bigazzi at warwick dot ac dot uk NA NA

### Class meetings

Activity Led by Time Building/Room
Lecture Schleimer Monday 11:00-12:00 MS.01 Zeeman
Support class Bigazzi Monday 15:00-16:00 LIB2 Library
Lecture Schleimer Tuesday 12:00-13:00 HO.51 Humanities in week one and then MS.01 Zeeman in weeks two to nine.
Support class Te Winkel Tuesday 13:00-14:00 B2.04/5 ScienceCconcourse
Lecture Schleimer Wednesday 9:00-10:00 HO.51 Humanities in weeks one to five and then MS.01 Zeeman in weeks six to ten.

### Reference materials

We will closely follow the first chapter of the book Algebraic topology, by Allen Hatcher. The book is available from Hatcher's website, and can also be purchased from the university bookshop or on-line.

Links to the Lecture Capture audio files, and to the discussion forum, are on the module's Moodle page.

### Example sheets

See the schedule for the example sheets.

In addition to the exercises prepared for this class, please note that Hatcher's book contains many interesting exercises. He has also given additional exercises. Here is the web-page for this module as taught by Professor Mond in 2012.

### 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, 2% (at most) may be earned every week (starting the second week) by turning in one of the three indicated exercises. These will be marked by a TA with a score of 0, 1, or 2. Please let me (Saul) know if any of the problems are unclear or have typos.

Homework solutions must be placed in the dropoff box (near the front office), by 14:00 on Thursdays. No late work will be accepted.

Please write your name, the date, and the module code (MA3F1) at the top of the page. If you collaborate with other students, please include their names.

Solutions typeset using LaTeX are preferred. Each problem should require at most one side of one page. If you find you need more space then write out a complete solution and then rewrite with conciseness in mind.

### 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.