The homework of week 12 has been graded and can be found in an envelope in my (Stefan's) mailbox. Make sure to collect it and bring all your graded homework to the exam. can be collected in my (Stefan's) office. I can send you an overview of the homework grades (including the average); send me an email including your name and student number and I'll reply with the overview as soon as possible.
Teacher: Gabriel Zalamansky, office 225, g.s.zalamansky(at)umail.leidenuniv.nl
Teaching assistant: Stefan van der Lugt, office 242 238, stefanvdlugt+iat(at)gmail.com
Lectures: 15:45  17:45 on Tuesday from 15 September to 15 December. There will be no lecture on 3 November.
Grading: there will be a homework assignment every week (12 assignments in total), and an oral exam at the end of the course. The exam counts for 60% towards the final grade, and the homework for 40%. The lowest homework grade will not count; that way it is possible to miss one assignment (because of absence, illness, a busy schedule, ...) and still get a maximal grade.
The oral exams will be on 25 and 26 January. The full schedule can be found here. The exams are in office number 240.
It is a 30mn oral. We will begin with (sometimes deliberately vague) questions about the lectures and the homeworks. You are expected to have a decent stack of examples (ie the most classical spaces : spheres, projective spaces, torus, Mobius band, Klein bottle, bouquet of circles...).
You should have an idea of which theorems are the most important and what hypothesis are needed.You will not be asked to reproduce the full proofs of the theorems but you are expected to be able to give an outline of them, the ideas that are used etc..
By default, the definitions and conventions in Lee's book stand. You should be aware of when and why this is needed. But at some point (eg for covering spaces and Galois theory) we relaxed them. You should be able to identify exactly when and what it implies.
All the homeworks are considered to be part of the Lectures. You should bring them with you so we can discuss them.
If time permits we will move on to a short exercise.
Lecture 1 

Lecture 2  
Lecture 3 

Lecture 4 

Lecture 5 

Lecture 6 

Lecture 7 

Lecture 8 

Lecture 9 

Lecture 10 

Lecture 11 

Lecture 12 

Lecture 13 

Students are encouraged to work on solving the homework problems together, but everybody has to write down the solutions individually. Copying another student's solutions is not acceptable and may result in a lower grade.
Homework has to be handed in on the Tuesday of the next lecture, either in class or in the mailbox of Stefan van der Lugt found in the common room at the second floor of the Snellius building. It is also possible to mail the homework, but please send your homework to Stefan's address found at the beginning of this page. If you send the homework by mail please send a (single) PDF file typeset in LaTeX. Scans will not be accepted. If you decide to hand in handwritten homework then make sure everything is legible; if it takes too long to decypher your handwriting your homework will not be graded. LaTeX is always fine!
Homework that is handed in too late will not be graded.
Homework  Deadline  Remarks 
Homework 1  22 September  Exercise 3: in the hint: replace 'positive' by 'nonnegative'. 
Homework 2  29 September  You may freely use the result of exercise 3 in exercise 2. 
Homework 3  6 October  Exercise 3: \(G\) is a topological group and the action of \(G\) on \(X\) is continuous. You may assume that \(X\) is Hausdorff. 
Homework 4  13 October  Exercise 3: \(p\) is surjective (some authors do not include this in the definition of a covering map). Also: replace 'compact' by 'compact and Hausdorff' everywhere (the French word 'compact' means 'compact and Hausdorff'; the English 'compact' translates to 'quasicompact' in French). 
Homework 5  20 October  Only 3 exercises this week; please do them all for a maximum grade! In exercise 2 the covering spaces are assumed to be connected. 
Homework 6  27 October  This week there are only two exercises, and you have to do both for a maximum grade. 
Homework 7  10 November  Again, hand in all 3 exercises. 
Homework 8  17 November  Again, hand in all 3 exercises. 
Homework 9  24 November  Again, hand in all 3 exercises. 
Homework 10  1 December  Only 2 exercises this week. 
Homework 11  8 December  Hint for exercise 2: use MayerVietoris! You are allowed to use the fact that the homology of \(S^1\) is given by \[H_n(S^1) = \left\{\begin{array}{ll}\mathbb{Z} & n=0,1\\0 & n\geq 2. \end{array}\right.\] 
Homework 12  15 December  You are allowed to use the fact that the MayerVietoris sequence is natural. See Wikipedia for more details. 
Homework 13    Some exercises involving theory from the last lecture. These exercises are not graded but feel free to ask any questions you have. 