Award details
Daniel Hudson
Department: Mathematics & Statistics
Faculty supervisor: Dr. Heath Emerson
Abstract
"I will be conduction research into equivariant K-theory modules. The goal of the project is to construct interesting examples of spaces equipped with an action the higher-dimensional compact torus T. Such a ‘T-space’ has an associated T-equivariant K-theory module associated to it. I aim to understand how to classify such modules and to apply the classification to the geometric examples. Secondly, I aim to build on this background work to construct examples of T-spaces in which one has a natural T-equivariant symmetry. Such a symmetry has an invariant associated to it, which can be interpreted in two ways by the work of the supervisor Emerson (and co-authors). One interpretation is geometric, and involves the fixed-point manifold of the symmetry. The other is global and homological in nature, and involves the module trace of the module map on T-equivariant K-theory induced by the symmetry. The equality of the two description is an equivariant version of the Lefschetz fixed-point formula, which is already a published result. But there lack examples of situations where it applies. My goal is therefore to construct such examples."
