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Geometry 2 (Geom2)
Provider: Faculty of Science

Activity no.: 5569-22-07-31 
Enrollment deadline: 16/11/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time21.11.2022, at: 08:00 - 27.01.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserHenrik Schlichtkrull    E-mail address: schlicht@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupB
Exam requirementsA mandatory assignment must be approved before the exam. The assignment is to be handed in no later than two weeks before the exam week.
Exam formOral examination, 30 minutes
Exam form30 minutes preparation, 30 minutes oral examination including grade determination
Exam detailsInformation will follow
Exam aidsAll aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures35.00
Preparation142.00
Theory exercises28.00
Exam1.00
Sum206.00
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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