Mathematics: Introduction to Algebraic Topology

This course provides a broad introduction to algebraic topology, the branch of mathematics that investigates properties of spaces preserved under continuous transformations. You will explore central concepts such as homotopy, fundamental groups, covering spaces, and the classification of compact surfaces.

Course content includes

• Homotopy theory, the fundamental group, covering spaces
• The Brouwer fixed point theorem, the Borsuk-Ulam theorem
• Deformation retracts, fundamental groups and homology of surfaces
• Surgery of manifolds, also called "cutting and pasting"
• Construction and classification of compact surfaces.

The course is an alternative-compulsory course within the Master’s programme in at Lund University. It may be suitable for interested students at Bachelor’s level. The course is also available as a stand-alone course.

Teaching consists of lectures and seminars. You will collaborate in small groups on a compulsory assignment, which is presented orally to the whole class. The course encourages active participation and cooperative problemsolving. Assessment includes a group presentation and an oral exam. The oral exam determines the final grade and can be retaken if necessary.

Algebraic topology plays a significant role in advanced mathematics and theoretical physics. This course prepares you for further study in geometry, topology, and mathematical physics, while strengthening your ability to think abstractly and communicate sophisticated mathematical ideas.

Entry requirements

For admission to the course, English 6/B as well as at least 90 credits, with at least 60 credits in mathematics are required, including knowledge corresponding to the courses MATB22 Linear Algebra 2, 7.5 credits, MATB23 Analysis in Several Variables 2, 7.5 credits, and MATM33 Differential Geometry, 7.5 credits.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 21,250
First payment: SEK 21,250

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.