Faculty of Science

Geometry 2 (Geom2)
Provider: Faculty of Science

Activity no.: 5569-21-07-31
	Enrollment deadline: 17/11/2021

Place

Department of Mathematical Sciences

Date and time

22.11.2021, at: 08:00 - 30.01.2022, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Henrik Schlichtkrull E-mail address: schlicht@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 2

Scheme group

Exam form

Course participation

Exam form

Oral examination, 30 minutes

Exam details

30 minutes of preparation before the exam

Grading scale

7 point grading scale. For PhD students: Passed / Not Passed

Course workload

Course workload category	Hours
Lectures	35.00
Preparation	142.00
Theory exercises	28.00
Exam	1.00

Sum	206.00

Content

The following subjects are covered.

1. Differentiable manifolds in Euclidean spaces.
2. Abstract differentiable manifolds.
3. Tangent spaces, differentiable maps and differentials.
4. Submanifolds immersions and imbeddings
5. Vector fields.
6. Lie groups and Lie Algebras
7. Differential forms.
8. Integration; Stokes' Theorem

Learning outcome

Knowledge:
Central definitions and theorems from the theory

Skill:
- Decide whether a given subset of R^n is a manifold
- Determine the differential of a smooth map
- Work with tangent vectors, including the Lie algebra of a Lie group
- Utilize topological concepts in relation with manifolds
- Find the Lie bracket of given vector fields
- Work with exterior differentiation and pull-back of differential forms

Competences:
- In general to perform logical reasoning within the subject of the course
- Give an oral presentation of a specific topic within the theory as well as a strategy for solving a specific problem

Literature

See Absalon.

Teaching and learning methods

5 hours of lectures and 4 hours of exercises per week for 7 weeks.

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