Title: Measured foliations at infinity of quasi-Fuchsian manifolds close to the Fuchsian locus
Speaker: Diptaishik Choudhury (University of Luxembourg)
Date: 04 September 2023
Time: 4:00 pm
Venue: MS teams (online)
Given a closed, oriented surface with genus greater that 2, we study quasi-Fuchsian hyperbolic 3-manifolds homeomorphic to this surface
times the interval. Different properties of these manifolds have been carefully studied in previous important works on 3 manifold geometry
and topology and some interesting questions about them still remain to be answered. In this talk, we will focus on a new geometric invariant
associated to them which we call the measured foliations at infinity. These are horizontal measured foliations of a holomorphic
quadratic differential ( the Schwarzian derivative ) associated canonically with each of the two connected component of the boundary at
infinity of a quasi-Fuchsian manifold. We ask whether given any pair of measured foliations (F,G) on a surface, is there a quasi-Fuchsian
manifold with F and G as it measured foliations at infinity. The answer is affirmative under certain assumptions; first, (F,G) satisfy the
property of being an “arational filling pair” and second, the quasi-Fuchsian manifold should be very close to being “Fuchsian” .
The goal of this talk would be introducing the concepts and outlining the proof idea.