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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
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.