Topology is a qualitative study of shapes and other mathematical objects.
It has evolved from features of geometry where specific measurments are not relevant. Modern topology uses tools from algebra and heavily interacts with other branches of mathematics such as dynamical systems, analysis, or algebraic geometry. Click on the following links to find out what kinds of things topologists like to think about. Euler characteristic critical points on the torus Several faculty members work in an area called Geometric Group Theory. The idea is to try to understand abstract groups by representing them as symmetry groups of nice spaces and then to study the topology and geometry of these spaces.