Description of Research Interest (Non-Technical version)

Topology is a large branch of theoretical (or “pure”) mathematics closely related to geometry. Like geometry, topology is a very visual subject. Instead of working with numbers, symbols and formulas, topologists and geometers study and compare objects in space. The difference between topology and geometry lies in the rules used to compare these objects. Loosely speaking, topologists have more relaxed rules than geometers. While geometers prefer rigid motions, topologists allow objects to be bent, stretched or twisted¾as long as they are not broken or torn. Thus, a topologist considers a circle and a square to be the same, since one can be transformed into the other by bending and stretching¾as can be easily demonstrated with a piece of string or wire. Read More

Description of Research Interest (Technical version)

My research area is geometric topology¾primarily the topology of manifolds. Manifold topology is frequently broken into the following sub-areas: low dimensional (2- and 3-manifolds), 4-dimensional (an area unto itself), high dimensional (finite dimensions >4), and infinite dimensional topology. I have done a little work in low dimensions, and a little more in dimension 4 (including my Ph.D. thesis). I maintain a strong interest in 4-manifold topology, and hope to get back to some problems in that area soon. Infinite dimensional (Hilbert cube) manifolds play a role in some of my recent work. However, the largest part of my research has involved high dimensional manifolds.Read More