MAT9530 – Algebraic Topology I
Schedule, syllabus and examination date
Changes in the course due to coronavirus
Autumn 2020 we plan for teaching and examinations to be conducted as described in the course description and on semester pages. However, changes may occur due to the corona situation. You will receive notifications about any changes at the semester page and/or in Canvas.
Spring 2020: Teaching and examinations was digitilized. See changes and common guidelines for exams at the MN faculty spring 2020.
The course gives an introduction to algebraic topology, with emphasis on the fundamental group and the singular homology groups of topological spaces.
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 to the course
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.
Recommended previous knowledge
- 10 credits overlap with MAT4530 – Algebraic Topology I.
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Final oral examination.
In addition, each PhD candidate 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.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more: