Geometry and topology at UH center around the study of manifolds, with the incorporation of methods from algebra and analysis.

The department conducts research into many topics in or related to geometry and topology. These include the following:

- low dimensional differential geometry and topology;
- knot theory;
- hyperbolic structures;
- infinite groups;
- the Novikov conjecture;
- the Baum-Connes conjecture;
- non-commutative differential geometry;
- geometric quantization;
- symplectic topology;
- index theory and spectra of operators associated with manifolds;
- pure and applied control theory;
- sub-Riemannian geometry;
- singularities;
- index theory of compact transformation groups;
- equivariant cobordism and surgery;
- equivariant cohomology.

##### Visitors and Friends

Colleagues who have visited us in recent years include: Greg Brumfiel, Robert Gardner, Richard Hamilton, Jerry Kaminker, Jerrold Marsden.