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Differential Geometry Seminar
Differential Geometry Seminar
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
Organizers
Kenji Fukaya
, Lynn Heller
, Sebastian Heller
, Kotaro Kawai
,
Enric Sole Farre
Speaker
Xiaolong Han
Time
Tuesday, April 28, 2026 2:30 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
Let M be a closed hyperbolic manifold. A sequence of closed, smoothly immersed hypersurfaces in M (up to homotopy and commensurability) is asymptotically geodesic if they are eventually totally geodesic. We show that if M contains such a sequence, its fundamental group is virtually special and thus a linear group with integer coefficients. If, in addition, M is arithmetic of type I, we build a sequence of asymptotically geodesic, strongly filling hypersurfaces that are equidistributing in the Grassmann bundles, where strongly filling implies a hypersurface having essential intersection with every geodesic.
This partially answers a question of Ben Lowe and Fernando Al Assal regarding the gap of hypersurfaces in higher dimensional hyperbolic manifolds and is a joint work with Ruojing Jiang.
This partially answers a question of Ben Lowe and Fernando Al Assal regarding the gap of hypersurfaces in higher dimensional hyperbolic manifolds and is a joint work with Ruojing Jiang.
Speaker Intro
Xiaolong Han is an Assistant professor at Shanghai Institute of Mathematics and Interdisciplinary Sciences. Before joining SIMIS, he was a postdoc at Yau Mathematica Sciences Center at Tsinghua University. In 2021, he obtained his PhD degree from University of Illinois Urbana-Champaign. His research interest is low-dimensional manifolds and hyperbolic geometry.