Global topology of the space of d-pleated surfaces

In this talk, we define the notion of d-pleated surfaces, which is a higher rank generalization of the classical notion of (abstract) pleated surfaces in three dimensional hyperbolic space. We give a description of the global topology of the space of conjugacy classes of d-pleated surfaces. We also prove that every connected component of the character variety contains exactly one connected component of the space of d-pleated surfaces. This is joint work with Sara Maloni, Giuseppe Martone, and Filippo Mazzoli.