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Topics in Algebraic Topology (BM)


Admission Requirements

The course Inleiding in de Algebraïsche Topologie is required.


This course is a sequel to the BSc course Inleiding in de Algebraische Topologie (IAT). The course will include a gentle introduction into homological algebra and the language of categories and functors. We introduce sheaves and their cohomology, discuss comparison theorems between singular, sheaf and Cech cohomology, and finish with some applications.

Course Objectives

The aim is to become acquainted with a number of important results and techniques in algebraic topology. After completing the course, the student will know how to apply these results and techniques in various situations in geometry.


You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.  

Mode of Instruction

Weekly lectures. Homework on a regular basis.

Assessment method

The final grade is based on homework (25%) and a final exam or retake (75%). The final exam is written or oral depending on the number of students. In order to pass the course the grade for the final exam or retake needs to be at least 5, and the weighted average of homework and final exam or retake needs to be at least 5.5. No mimimum grade for the homework is required in order to be allowed for the exam or in order to pass the course. The homework counts as a practical and there is no retake for it. In the event of a retake, the homework again counts for 25% for the final grade.

Reading list

We work from a syllabus that will be made available before the course starts. In addition to the syllabus, it is recommended to get hold of the following books:

  • W. Fulton, "Algebraic Topology, A first course", Springer Graduate Texts in Mathematics 153,

  • A. Hatcher, "Algebraic Topology", Cambridge University Press.


Please register for the course in MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December.

Please note that it is compulsory to register your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Not being registered for an exam means your grade will not be processed.


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By phone: +31 (0) 71 5 27 48 29