Charles ‘Terry’ Wall has made important contributions to differential topology. In 1959, he completed the classification of oriented smooth manifolds into cobordism classes. He then contributed to the development of ‘surgery’ theory, which permitted some classifications up to diffeomorphism.

In particular, he extended the theory to allow the fundamental group to be nontrivial. This raised algebraic problems which (for finite groups) were addressed by extending the classical theory of Hermitian forms. This permitted a study of free actions on spheres, with detailed results including some striking new examples. This work led to Terry becoming a recognised authority on the topology of manifolds.

Terry then turned to the study of smooth maps (singularity theory). He published significant papers on determinacy theorems. His extensive study of deformations of examples led to one side of the detailed analysis of topological stability appearing in a 1995 book with Andrew du Plessis. This led to diverse applications — hypersurfaces in projective space with symmetry; projection genericity of space curves; and transversality in families of mappings.