21 mar 2023 -- 13:30
Università degli Studi di Milano-Bicocca
The speaker will deliver the talk online via Webex platform and the meeting will be streamed also in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.
Meeting link below
Meeting number via webex (access code): 2741 555 4662
Abstract.
A geodesic plane in a hyperbolic 3-manifold is a totally geodesic isometric immersion from the hyperbolic plane. In a complete hyperbolic 3-manifold of finite volume, any geodesic plane is closed or dense, independently due to Ratner and Shah. Recently, there has been some exciting progress on generalizing this result to the infinite volume setting. In this talk, I will restrict to the case of a geodesic plane contained in an end of a quasifuchsian manifold. In this case, the topological behavior of the plane depends on the bending lamination. In particular, I will discuss the existence of exotic roofs, which are geodesic planes that accumulate on the boundary of the end, but cannot be separated from it by a support plane. A necessary condition is the existence of exotic rays for the bending lamination, which are geodesic rays that intersect the lamination recurrently, but are not asymptotic to any leaf of the lamination.