Topology is now a very broad area with links to Physics and Group Theory at its extremes. The primary topologists and their current projects are as follows.

John Jones is continuing his work, in collaboration with Ralph Cohen and Graeme Segal, on the study of the topology of the various moduli spaces which arise in gauge theory.

Colin Rourke who works in three areas. Group theory; classification of classical knots and links (together with Roger Fenn and Brian Sanderson) and singularity theory (together with Brian Sanderson).

Daan Krammer's research is centred around the following questions: Is the mapping class group linear? Does there exist a polynomial algorithm distinguishing links in three-space? The motivation and intuition of these questions comes from topology, but Daan Krammer's methods are combinatorial and comparable to those seen in representation theory.