MA4J7 Cohomology and Poincaré duality
Term II 2018-2019

Module Description

This module, MA4J7 (cohomology and Poincaré duality), has as its prerequisites MA3F1 (introduction to topology) and MA3H6 (algebraic topology).

Cohomology is a dual theory to homology; it continues our development of algebraic tools for the study of topological spaces. Cohomology is a richer, more algebraic, theory than homology is because it has a naturally defined ring structure coming from the cup product. It is also a key tool in the modern proof of Poincaré duality for manifolds.

The material covered in this module is essentially required for advanced study in the fields of topology, differential geometry, algebraic geometry, algebraic number theory, and others.

Schedule

The schedule has a planned list of topics, organized by week. We will change the schedule as necessary, as we work through the material. Example sheets will be posted about every two weeks.

Lecturer

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 Fridays 15:00-16:00
Igor Sikora NA igor dot sikora at warwick dot ac dot uk NA NA

Class meetings

Activity Led by Time Building/Room
Lecture Saul Schleimer Monday 10:00-11:00 B3.02 Zeeman.
Support class Igor Sikora Tuesday 14:00-13:00 C1.06 Zeeman.
Lecture Saul Schleimer Wednesday 12:00-13:00 B1.01 Zeeman.
Lecture Saul Schleimer Thursday 11:00-12:00 B3.01 Zeeman.

Reference materials

We will closely follow the third chapter of Allan Hatcher's book. Other references include Spanier's book (a classic), Peter May's book (concise), Rotman's book (gentle), tom Dieck's book (modern), ...

Here is a link to the discussion forum. You can also find a link to this on the on the module's Moodle page.

Example sheets and assessed work

See the schedule for the example sheets.

There is no assessed work. However, the exam will be closely based on the example sheets.

There are also many excellent problems in Hatcher's book.

Exam

The exam will be 100% of your mark. The exam will be closed book. Here are the exam papers for this module from the last five years.

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.