## MA3H6 Algebraic topology Term II 2013-2014

### Module Description

This module, MA3H6 (Algebraic topology), is a continuation of, and has as its only prerequisite, MA3F1 (Introduction to topology). Here we will begin the study of homology: a collection of algebraic invariants of topological spaces. Though the homology groups $$H_k(X)$$ of a space $$X$$ are more difficult to define than the homotopy groups $$\pi_k(X)$$ and, in some technical sense, record a simpler kind of information, homology scores over homotopy in two important respects:

1. It is far easier to compute.
2. It generalizes more directly to other areas of mathematics.

The material covered in this module is directly relevant to MA3H5 (Manifolds) and MA4J7 (Cohomology and Poincaré duality), as well as to MA4A5 (Algebraic geometry) 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 38/B2.14 s dot schleimer at warwick dot ac dot uk 024 7652 3560 Friday 15:10-16:00
Mark Bell 38/B0.15 m dot c dot bell at warwick dot ac dot uk NA NA
Ian Vincent 38/B0.15 i dot vincent at warwick dot ac dot uk NA NA

### Class meetings

Activity Led by Time Building/Room
Lecture Schleimer Monday 10:00-11:00 38/B3.03
Support class Vincent Monday 11:00-12:00 38/B3.01
Support class Bell Wednesday 10:00-11:00 38/B1.01
Lecture Schleimer Thursday 10:00-11:00 38/MS.04
Lecture Schleimer Friday 14:00-15:00 38/B3.03

### Reference materials

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

Another book on this topic, with a very different viewpoint, is Algebraic topology, a first course by William Fulton.

### Example sheets

See the schedule for the example sheets.

In addition to the exercise prepared for this class, please note that Hatcher's book contains many interesting exercises. He has also given additional exercises. Here are the exercises from Prof. Mond's module in 2012: revision on Abelian groups and exercise sheets one and two.

### 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 a single worked exercise. Please let me (Saul) know if any of the problems are unclear or have typos.

Homework solutions must be turned in to Ian Vincent, or placed in his supervisor's pigeonhole, by 12noon on Mondays. No late work will be accepted. Please write your name, the date, and the problem you are solving at the top of the page. If you collaborate with other students, please include their names. Solutions typeset using LaTeX are preferred. Please limit your solution to one piece of paper -- if more space is needed 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.