## GEOMETRY 2, FALL 2011

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

21/11 Monday 1.1-1.3

22/11 Tuesday 1.4-1.6

25/11 Friday 1.7-1.8

28/11 Monday 2.1-2.3

29/11 Tuesday 2.4-2.7

2/12 Friday 2.8-2.10

5/12 Monday 3.1-3.5

6/12 Tuesday 3.6-3.8

9/12 Friday 3.9-3.10

12/12 Monday 4.1-4.3

13/12 Tuesday 4.3-4.5

16/12 Friday 4.6-4.8

19/12 Monday 5.1-5.5

20/12 Tuesday 5.6-5.11

23/12 Friday Cancelled

2/1 Monday Lectures this week are replaced by a mandatory written assignment

3/1 Tuesday Lecture cancelled (but not exercises)

6/1 Friday Lecture cancelled (but not exercises)

9/1 Monday 6.1-6.4

10/1 Tuesday 6.5-6.8

13/1 Friday 6.9-6.10

### 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.

22/11 Tuesday Exercises cancelled (but not lectures)

25/11 Friday P1

29/11 Tuesday P2

2/12 Friday P3

6/12 Tuesday P4+E1

9/12 Friday P5+E2

13/12 Tuesday P6+E3

16/12 Friday P7+E4

20/12 Tuesday P8

23/12 Friday Cancelled

3/1 Tuesday P9+E5.

6/1 Friday P10+E6

10/1 Tuesday P11+E7

13/1 Friday P12+E8

17/1 Tuesday E9+E10

20/1 Friday E11+E12

### MANDATORY EXERCISE ASSIGNMENT

There is one mandatory written assignment during the course.
It will be web-posed Monday January 2, and the deadline for
return is Friday January 6 at the start of the exercise class.

### EXAM

26-27/1 Thursday-Friday: Oral exam

### PROBLEM PROGRAMS

Select problems from the following list. The problems
cover the mentioned sections.

P1: 1.1-1.4, Exercises 1.1-1.7

P2: 1.5-1.8, Exercises 1.8-1.17

P3: 2.1-2.5, Exercises 2.1-2.10

P4: 2.6-2.10, Exercises 2.11-2.15

P5: 3.1-3.6, Exercises 3.1-3.5

P6: 3.7-3.10, Exercises 3.6-3.10

P7: 4.1-4.4, Exercises 4.1-4.8

P8: 4.5-4.8, Exercises 4.9-4.15

P9: 5.1-5.6, Exercises 5.1-5.5

P10: 5.7-5.10, Exercises 5.6-5.12

P11: 6.1-6.5, Exercises 6.1-6.7

P12: 6.6-6.9, Exercises 6.8-6.14

### 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)