# Topology and Foliation Theory

A primary theme of topology is to associate algebraic structures to a topological space with the goal of determining if such structures allow one to decide whether two topological spaces are equivalent. One goal is to classify the topological structures of manifolds. Topologists in our department do research in characteristic classes, low dimensional topology, especially 3-manifolds, foliations of manifolds, connections with dynamical systems, and Lie groups.