Topologie en Meetkunde, periode 3 en 4, 2006

(under permanent change)

This is the web-page for the course Topologie en Meetkunde, 2006.

HERE ARE THE RESULTS OF THE EXAMS (the .pdf file is available HERE).

If you want to see your exam (and I advise you to have a look!) and/or for any questions regarding the exam, please contact Camilo Arias Abad (e-mail:, office: 415).

- The course is given every Monday, from 13:15 to 15:00, in BBL 105b. Lecturer: Marius Crainic.

(Het college wordt gegeven op maandagmiddag van 13.15 tot 15.00 door dr. M. Crainic in BBL 160.)

- The exercise classes will take place every Thursday, from 13:15 to 15:00 in MG 012. In charge: Camilo Arias Abad.

(Het practicum is op donderdag van 13.15 tot 15.00, in MG 012. De practicumleider is Camilo Arias Abad.)

- Text book: "Topology" by James A. Munkres, 2-nd edition.

- Rules for the examniation: there are two exams, A and B. Both of them have to be passed, with a minimum mark of 5 for each one of them, and with an average of at least 6. One part of the exam is not valid for more then a year. There will be one chance to repeat the exam.

(Tentamenregeling: er zijn twee deeltentamens, A en B. Deze hebben geen zelfstandige betekenis: om het vak te halen moet over beide tentamens een gemiddelde van minstens 6 worden gehaald; met dien verstande dat de uitslag van beide tentamens minstens 5 moet zijn. Een deeltentamen blijft niet geldig tot volgend jaar. Er is een herkansing over de gehele stof.)

First part (February 6- April 17)

6 February (week 6): Lecture 1

13 February (week 7): Lecture 2

20 February (week 8): Lecture 3

27 February (week 9): Lecture 4. also: solutions to some of the previous exercises.

6 March (week 10): Lecture 5

13 March (week 11): Lecture 6

20 March (week 12): No lecture

27 March (week 13): Lecture 7

3 April (week 14): Lecture 8

10 April (week 15): Lecture 9. More solutions to some of the previous exercises. Also an errata for the first 8 lectures.

17 April (week 16): Exam week (first exam).

Second part (April 24-July 3)

Here is what we have discussed in the second semester, together with some lecture notes (the lecture notes that have previously been on this web-page have not been changed. The last notes are on the Seifer-van Kampen theorem).

- Quotient topologies . The notes contain a bit more then it has been done in the lectures: some of the exercises are solved in the notes, and more examples are presented, in a greater detail.

- Attaching cells . (presented in lectures 12, 13, and half of 14).

- Topological manifolds, surfaces, connected sums, connected sum of g tori (the torus with g wholes), connected sum of h projective planes: definitions. There are no notes for this part (see the text book).

- The fundamental group . The notes contain a bit more information about categories and groupoids (which was not presented in the course, and is not required for the exam).

- Covering spaces and the fundamental group of the circle. Here are the notes .

- The Seifert-van Kampen theorem . The notes contain more examples then what has been presented in the lectures, and also a description of some general steps to follow for computing fundamental groups.

- Here are some exercises that have been handed out in Lecture 17 (June 19).

- Here is the table of content for all the lecture notes (first and second part of the course).

Here is the schedule:

24 April (week 17): Lecture 10

1 May (week 18): Lecture 11

8 May (week 19): Lecture 12

15 May (week 20): Lecture 13

22 May (week 21): Lecture 14

29 May (week 22): Lecture 15

5 June (week 23): No lecture (pinksteren)

12 June (week 24): Lecture 16

19 June (week 25): Lecture 17

26 June (week 26): Lecture 18

6 July (week 27): Exam week (second exam). One may use the lecture notes during the entire exam (but not the text book).