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Introduction to algebraic topology


Admission requirements

Admission requirements: the Leiden bachelor courses Algebra 1 & 2, Lineaire Algebra 1 & 2, Topologie, or their equivalents.


We continue the study of fundamental groups and covering spaces that was started in the course Topologie. Among other things we discuss winding numbers, the Van Kampen theorem, the Borsuk-Ulam theorem. We will also discuss applications of topology in algebra (for example, the result that a subgroup of finite index of a free group is free).

Course objectives

At the end of the course the student will have learnt about some of the fundamental notions and results of algebraic topology. The student will be able to apply the learnt notions and results in several not-too-difficult situations.

Mode of instruction

Weekly lectures. Homework on a regular basis.

Assessment method

Homework, and a final written or oral exam (depending on the number of participants). The homework counts for 25%, the final exam for 75%. To pass the course a minimum of 5 is required for both homework and final exam.


W. Fulton, "Algebraic Topology, A first course", Springer Graduate Texts in Mathematics 153. Available from the university network via SpringerLink.


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Contact information

By e-mail: rdejong@math.leidenuniv.nl
By phone: +31 (0) 71 5 27 71 40