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Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds

组织者

深谷賢治 , 杨琳 , 塞巴斯蒂安·赫勒 , 河井公大朗 , Enric Sole Farre

演讲者

韩肖垄

时间

2026年04月28日 14:30 至 16:30

地点

A3-4-301

线上

Zoom 293 812 9202 (BIMSA)

摘要

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.