KTH    Matematik

## SF2735: Homologisk algebra och Algebraisk Topologi, Höst 2011

Homework number 4 is availbale here. It is due on Monday December 19.

If you would  like to get the gread A in the course, you are   required to  have a friendly 15 min  conversation with me. During the conversation I would like you to tell me your favourit theorem or problem in the course and why it is so.  Please send me an e-mail with a suggestion when you would like to meet.

For those who would like to get a grade before Christmas,
you should turn in homeowrk nr. 4 by Friday Decemeber 16.
For those who would like to get a grade A before Christmas
I will be available for friendly conversations on:
Thursday Dec 15, 14:00-15:20
Friday Dec 16, 10:00- 13:00

Lecture on Thursday Dec 8 is canceled.
We will continue on Dec 15 between 8:15 and 11:00 (3x45 minutes). This will be the last lecture. There will be  a 45 min of excercise session after the lecture (11:15-12:00).

Torsten Ekedahl died last week. Because of this sad event, I will continue in his place the topology part of the course.

The third homework is available here.
The second homework is available here
The first homework set is available here.

The  time for the course: Thursdays 8:15-10:00
in room 3733
In principle
every second week after the lecture at 10:15-11:00 there will be an excercise session.  It will be run by Ornella Greco. The following table contains detailed schedule:

 Lecture Content Recomended Excercises 27 Oct EXCERCISE SESSION, 10:15-11:00 27 Oct LECTURE, T. Ekedahl 20 Oct EXCERCISE SESSION, 10:15-11:00 20 Oct LECTURE. 13 Oct LECTURE. 6 Oct EXCERCISE SESSION, 10:15-11:00 6 Oct LECTURE. 29 Sept EXCERCISE SESSION, 10:15-11:00 29 Sept LECTURE. Chapter 3 and part of chapter 4. Injective and projective modules, snake lemma, homology. 22 Sept LECTURE. Part of chapter 2 and Chapter 3. Exactness and propoerties of the Hom functor, exactness. Projective and injective modules 2.3.1, 2.3.3, 2.3.5, 3.4.1, 3.4.1, 3.4,5, 3.4,6, 3.4.7, 3.4.9,  3.4.11 13 Sept LECTURE. Chapter 2. Chain complexes as an abelian category.  Definition of chain complexes and maps between them. Examples and operations of chain complexes 30 Aug LECTURE. Chapter 1. Modules as an ablelian category. Definitions examples and properties. The group of module homomorphisms 1.8.2, 1.8.6, 1.8.13, 1.8.15, 1.8.20, 1.8.25, 1.8.27, 1.8.29

The course is devided into two parts:
Part 1: homologiacal algebra
Part 2: Algebraic toplogy.
The first part will be  taught by Wojciech Chacholski. The last lecture of this part will be given on October 25.
The second part will be taught by Torsten Ekedahl.
There will be also excercises given every other week.

Here is a PDF file of the notes for the course.
T. Ekedahl's introductory notes to the course are available here.

Recommended literature for topology:
there are a lot of book available in the library. Here are some that one might use for an extra reading.
Genreal topology:
- "Outline of General Topology" by R. Engenlking
Alg Topology:
- "Algebraic Topology" by Allen Hatcher (also available on the net here)
- "Lectures on Algebraic Topology" by M. Greenberg
- "Algebraic topology, an introductory course" by Peter Hilton
- "Algebraic topology, a first course" by Max Agoston

Some literature for homological algebra:
Weibel "Homologisk Algebra", Hilton & Stammback "A course in homological algebra", Vick "Homology theory", Rotman "Introduction to Homological Algebra",