See also the course catalogue and (requires login) Absalon


Differentiable Manifolds, by Henrik Schlichtkrull. 2013 version.
ISBN 978-87-7078-353-8, Polyteknisk Boghandel.


(preliminary plan)
18/11 Monday 1.1-1.5
19/11 Tuesday 1.6-1.8
22/11 Friday 2.1-2.3
25/11 Monday 2.4-2.7
26/11 Tuesday 2.7-2.10
29/11 Friday The Grassmann manifold. Extra notes here

2/12 Monday 3.1-3.5
3/12 Tuesday 3.5-3.8
6/12 Friday 3.8-3.10
9/12 Monday 4.1-4.3
10/12 Tuesday 4.4-4.6
13/12 Friday 4.7-4.10
16/12 Monday 5.1-5.5
17/12 Tuesday 5.6-5.8
20/12 Friday 5.9-5.11

3/1 Friday No lecture. (See about a mandatory written assignment below)
6/1 Monday 6.1-6.4
7/1 Tuesday 6.5-6.8
10/1 Friday 6.9-6.10
14/1 Tuesday. Question session. AUD 6


Exercise classes are used for problem solving, and for presentation of exam questions by participants as preparation for the oral exam. There are 12 problem programs P1-P12 (see below), and 13 exam questions E1-E13 (also below). Further presentations will be planned once the exact number of students is known - the goal is that every student presents one question.

The exercise classes are conducted by Wolfgang Steimle and by Massimiliano Ungheretti.

19/11 Tuesday P1
22/11 Friday P2
26/11 Tuesday P3
29/11 Friday P4
3/12 Tuesday P5+E1
6/12 Friday P6+E2
10/12 Tuesday P7+E3
13/12 Friday Selected exercises with which you were behind+E4. Note that the remaing P-program has been postponed by half a week.
17/12 Tuesday P8+E5
20/12 Friday P9+E6
3/1 Friday No class. (See about a mandatory written assignment below)
7/1 Tuesday P10+E7+E8
10/1 Friday P11+E9+E10
14/1 Tuesday P12+E11+E12+E13


A mandatory written assignment replaces the teaching of January 3. It will be web-posed January 2, and must be returned by Tuesday January 7 at the start of the exercise class.


Select problems from the following list. The problems cover the mentioned sections. Emphasis will be on the highlighted problems.
P1: 1.1-1.4, Exercises 1.1-1.7. 3,4,5,7
P2: 1.5-1.8, Exercises 1.8-1.17. 11,12,13,15,17
P3: 2.1-2.5, Exercises 2.1-2.10. 4,5,6,7,9,10
P4: 2.6-2.10, Exercises 2.11-2.15. All
P5: 3.1-3.6, Exercises 3.1-3.5. 2,3,4
P6: 3.7-3.10, Exercises 3.6-3.10. 6,7,8,10
P7: 4.1-4.4, Exercises 4.1-4.8. 2,3,4,5
P8: 4.5-4.8, Exercises 4.9-4.15. 10,11,12,13
P9: 5.1-5.6, Exercises 5.1-5.5. 2,3,4
P10: 5.7-5.10, Exercises 5.6-5.12. 8,9,10,11
P11: 6.1-6.5, Exercises 6.1-6.7. 1,3,4,6
P12: 6.6-6.9, Exercises 6.8-6.14. 10,12,13,14


The oral exam is scheduled for Friday 24, but one day is not enough. Please see here

The scope of the exam is as follows: The student draws a question from the following list, and is allowed approximately 30 minutes of preparation. The examination lasts 25 minutes, of which 15-20 minutes will be spent on the presentation. After that questions will be asked in the entire curiculum of the course. At the end the student receives a grade.
The official language of the exam is English (but Danish will be accepted as well).


E1: Manifolds in R^n
E2: Abstract manifolds. Projective space.
E3: The Grassmann manifold.
E4: The tangent space of an abstract manifold
E5: Smooth maps and their differentials
E6: Submanifolds
E7: The orthogonal group is a Lie group
E8: Partition of unity
E9: Embedding in Euclidean space
E10: Connectedness and components
E11: Vector fields and Lie brackets
E12: The Lie algebra of a Lie group
E13: The Lie algebra of GL(n,R)