MM816: Geometry of Surfaces (5 ECTS)

STADS: 13005901

Level
Master's level course

Teaching period
The course is offered in the spring semester.
3rd quarter.

Teacher responsible
Email: duck@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM516.

Prerequisites:
None

Academic preconditions:
Basic knowledge of point set topology as well as curves and surfaces is assumed to be known. Basic knowledge of complex function theory is recommended.

Course introduction
The course introduces some important algebraic framework to describe the topology of surfaces, and the interplay between geometry and topology of surfaces via the Gauss-Bonnet Theorem.

Expected learning outcome
At the end of the course the student will be able to:

• reproduce the definitions within the scope of the course’s syllabus in a precise mathematical language
• reproduce results, together with complete proofs, within the scope of the course’s syllabus
• relate the results within the scope of the course’s syllabus to each other
• apply the theory to solve problems within the scope of the course's syllabus
• describe the constructions of delta-homology and singular homology, and the polygonal representation of surfaces
• combine concepts from algebra, topology and geometry to explain results within the scope of the course’s syllabus.

Subject overview

• Abstract topological surfaces
• Homotopical maps between surfaces
• Combinatorial representation of surfaces
• Surfaces as delta-complexes
• Homology
• Euler characteristic and the Gauss-Bonnet Theorem
• Classification of compact abstract surfaces

Literature

• Meddeles ved kursets start..

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Mandatory assignments prepared and presented during the course. The mandatory assignments are evaluated collectively, pass/fail, internal censorship by the lecturer. The mandatory assignments must be passed for the student to take the oral exam.
b) Oral examination, grades according to the Danish 7-point scale and external censorship.

Reexamination after 4th quarter. The exam form at the re-exam can be different than at the ordinary exam.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 18 timer
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.