|Date: Wednesday, April 13, 2022
Location: 3866 East Hall (4:00 PM to 6:00 PM)
Title: Pleated surfaces in PSL(d,C) and their coordinates
Abstract: Thurston introduced pleated surfaces as a powerful tool to study hyperbolic 3-manifolds. Passing to universal covers, a pleated surface is a map f from the hyperbolic plane into hyperbolic 3-space which is a totally geodesic immersion on the complement of geodesic lamination and is equivariant with respect to a representation from the fundamental group of a hyperbolic surface into the Lie group PSL(2,C) of orientation preserving isometries of hyperbolic 3-space.
For a fixed maximal geodesic lamination L, Bonahon described a holomorphic parametrization of the space of pleated surfaces with pleating locus L which in turn provides a holomorphic parametrization of an open subset of the character variety of PSL(2,C).
In this talk, we will discuss a generalization of this theory to surface group representations into PSL(d,C). In particular, we introduce a notion of d-pleated surface which is motivated by the theory of Anosov representations, and we define shear-bend-eruption coordinates for these representations.
This talk is based on joint work with Sara Maloni, Filippo Mazzoli and Tengren Zhang.
Speaker: Giuseppe Martone
Institution: U Michigan
Event Organizer: Spatzier Giuseppe Martone