TOPOLOGY AND GEOMETRIC GROUP THEORY

ABOUT TOPOLOGY AND GEOMETRIC GROUP THEORY

Geometric topology students research settings which mathematicians call a space. This branch of math emphasizes aspects that are most closely allied to classical geometry like distances, polyhedral objects that generalize intervals and triangles; manifolds that generalize planes, surfaces, and Euclidean spaces. Geometric group theory students research models of symmetries and rigid motions. It is applied when objects such as a molecule or a space exhibits symmetries or admits motions. The group of symmetries or motions reflects the geometry of the object or space on which it acts.