## Admission requirements

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

## Description

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 finitely generated free group is free and finitely generated). We will also treat singular homology.

## 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

The final grade is based on homework (25%) and a final exam or retake (75%). 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.

## Literature

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

John M. Lee, "Introduction to Topological Manifolds, second edition", Springer Graduate Texts in Mathematics 202.

Both books are available from the university network via SpringerLink.

## Brightspace/website

Brightspace will be used.

## Contact information

By e-mail: rdejong[at]math.leidenuniv.nl

By phone: +31 (0) 71 5 27 71 40