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The University of Southampton
Mathematical Sciences

Research project: Profinite topology on non-positively curved groups

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A principal theme of Geometric Group Theory is the study of non-positively curved groups. A group G is non-positively curved if it acts by transformations (in a sufficiently good manner) on a space X, whose geometry is similar to the geometry of a Euclidean or Hyperbolic space. In the presence of such an action, the properties of X give a lot of information about the structure of G and vice-versa.

One of the most natural ways to study an infinite discrete group G is to look at its finite quotients. However, for some groups this approach is completely fruitless; e.g., there exist infinite groups which have no non-trivial finite quotients at all. To measure how well can a given group be approximated by finite groups, various 'residual properties' of groups, such as residual finiteness, conjugacy separability, etc., were introduced.

Non-positively curved groups tend to be relatively nice from this viewpoint, and this project concentrates on the interaction between the geometry of the group and its residual properties.

Related research groups

Pure Mathematics
Geometric Group Theory
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