## Content

Topology is a subject of fundamental importance in many branches of modern mathematics. Basically, it concerns properties of objects which remain unchanged under continuous deformation, which means by squeezing, stretching and twisting. Apples and oranges are topologically the same, but you can't deform an orange into a doughnut! More precisely, we can never deform in a continuous way a sphere (the surface of an orange) into a torus (the surface of a doughnut). Knots are also examples of topological objects, where a trefoil knot can never be deformed into an unknotted piece of string.

The aim of this module is to explore properties of topological spaces. To distinguish topological spaces we will consider topological invariants such as the fundamental group, which is a powerful way of using algebra to detect topological features of spaces.

The aim of this module is to explore properties of topological spaces. To distinguish topological spaces we will consider topological invariants such as the fundamental group, which is a powerful way of using algebra to detect topological features of spaces.

## Lecture Notes

The lecture notes for this course can be found by following the link below. They will be updated continually throughout the course.

**Note that this is the version of the course taught in the spring semester 2017.**- An introduction to Algebraic Topology
- Slides of the first lecture
- Slides about quotients of the unit square
- Slides about the organisation of the course
- One of the lectures was given on Valentine's Day. I made a little presentation for this occasion.

Exercises

Mock Exams

## Literature

*Crossley, M. D.: Essential Topology, Springer, 2010**Hocking, John G.; Young, Gail S.: Topology, Dover Publications, 1988**Bredon, Glen E.: Topology and Geometry, Springer, 1993**Hatcher, A.: Algebraic Topology, Cambridge University Press, 2002**Hatcher, A.: Notes on Introductory Point-set Topology*