Schedule, syllabus and examination date

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Course content

The course gives an introduction to algebraic topology, with emphasis on the fundamental group and the singular homology groups of topological spaces.

Learning outcome

After completing the course you:

  • can work with cell complexes and the basic notions of homotopy theory;
  • know the construction of the fundamental group of a topological space, can use van Kampen's theorem to calculate this group for cell complexes, and know the connection between covering spaces and the fundamental group;
  • can define the singular homology groups, and can prove their central properties, such as homotopy invariance, exactness and excision;
  • master the basic homological algebra associated to chain complexes and their homology, and can use simplicial and cellular homology to make effective calculations of homology groups;
  • understand enough category theory to give an axiomatic characterization of singular homology.

 

After having completed the course you will also be able to:

  • present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer

 

 

 

 

Admission

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Prerequisites

Formal prerequisite knowledge

None.

Recommended previous knowledge

MAT3500 – Topology/MAT4500 – Topology. It may also be useful to have MAT4510 – Geometric structures.

Overlapping courses

10 credits with MA362.

10 credits with MAT4530 – Algebraic topology I.

*The information about overlaps is not complete. Contact the department for more information if necessary.

Teaching

4 hours of lectures/exercises per week throughout the semester.

Examination

Final oral examination.

In addition, each PhD student is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

This course offers both postponed and resit of examination. Read more:

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

PhD

Teaching

Every spring

Examination

Every spring

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.