Appears in collection : 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

The notion of a d-pleated surface is a higher rank generalization 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.