This is the web-page for the course Topologie en Meetkunde, 2006.
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: firstname.lastname@example.org, office: 415).
(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.)
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).
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).