GEOMETRY 2, FALL 2012

See also the Study Information System SIS page and (requires login) Absalon

MANDATORY EXERCISE ASSIGNMENT: here (the return deadline, January 8, has passed). Solutions here

LECTURE NOTES

Differentiable Manifolds, by Henrik Schlichtkrull. 2012 version.
ISBN 978-87-7078-283-8, Polyteknisk Boghandel.

LECTURES

19/11 Monday 1.1-1.3
20/11 Tuesday 1.4-1.6
23/11 Friday 1.7-1.8
26/11 Monday 2.1-2.4
27/11 Tuesday 2.4-2.7
30/11 Friday 2.8-2.10
3/12 Monday 3.1-3.5
4/12 Tuesday 3.6-3.8
7/12 Friday 3.9-3.10
10/12 Monday 4.1-4.3
11/12 Tuesday 4.4-4.6
14/12 Friday 4.7-4.10
17/12 Monday 5.1-5.5
18/12 Tuesday 5.6-5.8
21/12 Friday 5.9-5.11

4/1 Friday The lecture is replaced by a mandatory written assignment (see below)
7/1 Monday 6.1-6.4
8/1 Tuesday 6.5-6.8
11/1 Friday 6.9-6.10
22/1 Tuesday. Question session (Aud 8, starts 13:15).

EXERCISE CLASSES

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, and 12 exam questions E1-E12. The plan below may be revised when the number of students is known - the goal is that every student presents one question.

20/11 Tuesday Exercises cancelled (but not lectures). They are replaced by extra classes up to the exam.
23/11 Friday P1
27/11 Tuesday P2
30/11 Friday P3
4/12 Tuesday P4+E1 (Anna)
7/12 Friday P5+E2 (Jens Jacob)
11/12 Tuesday P6+E3 (Jason)
14/12 Friday P7+E4 (Rie)
18/12 Tuesday P8
21/12 Friday P9+E5 (Ji Yoon)
4/1 Friday P10+E6 (David)
8/1 Tuesday P11
11/1 Friday P12+E7+E8 (Birger + Helle)
15/1 Tuesday E9+E10+E1 (Evgeny + Nikolaos + Konstantinos)
18/1 Friday E11+E12 (Thomas + Estibaliz)

MANDATORY EXERCISE ASSIGNMENT

There is one mandatory written assignment during the course. It will be web-posed Wednesday January 2, and must be returned by Tuesday January 8 at the start of the exercise class.

PROBLEM PROGRAMS

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

EXAM

23-24/1 Oral exam. Please see the schedule in ABSALON.

EXAM QUESTIONS

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