RCD-spaces arise naturally from optimal transport theory by the work of Otto-Villanni-Sturm. Moreover, these spaces have a very rich (local) analysis, and several properties of Riemannian manifolds hold for these spaces. But so far the global underlying topological structure of RCD-spaces is not fully understood. 

 

In this talk we consider RCD-spaces with a lot of symmetry, that is a large Lie group acting on it by measure preserving isometries, and fully describe the underlying topological structure. We prove this by taking ideas from optimal transport to construct a canonical space transverse to the orbit. Moreover, I also present a systematic method of constructing such RCD-spaces with high symmetry.

 

This is joint work with Jesús Núñez-Zimbrón and Jaime Santos-Rodríguez.