Topics on 3- and 4-dimensional manifolds.

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- to develop practical algorithms for recognising surfaces, knots and 3-dimensional spaces. These will be very useful for experimentation and to understand the computational complexity of such questions. - to understand the properties of minimal surfaces in 3-dimensional spaces of constant negative curvature, with applications to the complexity of knots and the structure of these spaces. - to develop a theory of 4-dimensional spaces which are covered by Euclidean 4-space. New techniques will be utilised, since the powerful methods of Freedman-Quinn do not apply to most such spaces.