Spaces with symmetry through the K-theoretic lens

K理论视角下的对称空间

20000

This project will serve as a contribution to the program of classifying spaces with desirable symmetry, as well as understanding examples of those spaces which classify important mathematical structures in their own right. The main tool we will utilize in this project is K-theory, a powerful machinery which has garnered popularity due to its close tie with string theory and condense matter physics and probes properties of spaces by their 'linear algebra'. We will in particular focus on homogeneous spaces, the building blocks of spaces with symmetry, and seek to give a computable K-theoretic characterization of those spaces where information about the symmetry and other properties of the underlying spaces can be gleaned independently. We will also study moduli spaces, which parametrize geometric and physical structures and come equipped with nice symmetry, and calculate their K-theory which is expected to unveil richer geometric information and thus inspire further research.