Algebraic invariants of spaces with group action

The project lies in the area of geometry and topology. A range of geometric
objects are relevant arising from homotopy theory, representation theory and
algebra more broadly.
To start with one may consider invariants that are invariant under feformations,
but one may go on to build the algebraic invariants using more geometric
methods. In certain circumstances these two approaches converge and a
complete model can be built in an algebraic setting. This is in the context of the
fact that equivariant homotopy theory is now quite well understood and ready
for this treatment. The aim is to give accessible means of calculation and access
to broad structural features. The test in this particular case is whether
calculations can be completed. For example one may seek a form of higher Smith
theory along the lines of Dwyer and Wilkerson.