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The University of Southampton
Mathematical Sciences

Research Group: Topology

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Research in Topology centres around Homotopy Theory and Toric Topology. Homotopy Theory is the study of the continuous deformations of topological spaces and the maps between them. Toric Topology is the study of topological spaces with well behaved toric symmetries. Both topics act as unifying forces for several areas of mathematics and these connections also feature prominently in our research. 

Research interests in the group broadly fall into two categories. 

  1. Polyhedral products. These are functorial generalisations of moment-angle complexes, which are central to toric topology. They unify a wide variety of of constructions from many different areas of mathematics, and the study of their homotopy theoretic properties has multiple applications. This is a new and rapidly growing subject with high impact.
  2. Unstable homotopy theory. This is the modern formulation of classical homotopy theory. It is concerned with fundamental spaces that are of enduring interest, such as spheres, Moore spaces, Lie groups, and manifolds. The methods have wider application, and we use them to study spaces that arise in other areas of mathematics and physics, such as gauge groups, free loop spaces and configuration spaces. 
Moebius link

The group welcomes applications for postgraduate studies. Please contact group members (email, telephone, or in person) for more information; and when ready, please apply through the Graduate School application page.

List of related projects to Topology
Related ProjectsStatus
Homotopy groups of manifoldsActive
Massey products in toric topologyActive
Symmetries of polyhedral productsActive
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