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Courses / Modules / MATH3080 Algebraic Topology

Algebraic Topology

When you'll study it
Semester 2
CATS points
ECTS points
Level 6
Module lead
Jelena Grbic
Academic year

Module overview

Topology is concerned with the way in which geometric objects can be continuously deformed to one another. It can be thought of as a variation of geometry where there is a notion of points being "close together" but without there being a precise measure of their distance apart.

Examples of topological objects are surfaces which we might imagine to be made of some infinitely malleable material. However much we try, we can never deform in a continuous way a torus (the surface of a bagel) into the surface of the sphere. Other kinds of topological objects are knots, i.e. closed loops in 3-dimensional space. Thus, a trefoil or "half hitch" knot can never be deformed into an unknotted piece of string. It's the business of topology to describe more precisely such phenomena.

In topology, especially in algebraic topology, we tend to translate a geometrical, or better said a topological problem to an algebraic problem (more precisely, for example, to a group theoretical problem). Then we solve that algebraic problem and try to see what that solution tells us of our initial topological problem. So to do topology you need to work equally well with both geometric and algebraic objects.

Linked modules

Pre-requisites: (MATH2003 AND MATH2039 AND MATH2049) OR (MATH2003 AND MATH2039 AND MATH2046)