My research interests are in three areas which are closely connected. They are

  1. Low dimensional geometric topology
  2. Differential geometry
  3. Geometric group theory

In area 1) my main interests are in 3-dimensional manifolds. See [1] below for a long expository article on the subject. The introduction should give some idea of the subject.

In area 2), I am interested in 3-dimensional hyperbolic geometry and minimal surface theory. See [2] below for a short paper which will give an introduction to some simple geometric ideas in the context of curves on surfaces.

The basic philosophy in area 3) is that ideas about infinite groups are significant if they arise from a geometrical context. I am interested in Kleinian groups and the associated geometry, topology and group theory. I am also interested in more abstract ideas about infinite groups, in particular the theory of negatively curved groups. Fundamental groups of closed surfaces and free groups are among the basic examples of such groups.

[1] The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487.

[2] Closed geodesics on surfaces, Bull. London Math. Soc. 14 (1982), 385-391 (with M.H. Freedman and J. Hass).