Trees of manifolds as boundaries of spaces and groups

Świątkowski, Jacek¹

¹ Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland

Geometry & topology, Tome 24 (2020) no. 2, pp. 593-622.

Résumé

We show that trees of manifolds, the topological spaces introduced by Jakobsche, appear as boundaries at infinity of various spaces and groups. In particular, they appear as Gromov boundaries of some hyperbolic groups, of arbitrary dimension, obtained by the procedure of strict hyperbolization. We also recognize these spaces as boundaries of arbitrary Coxeter groups with manifold nerves and as Gromov boundaries of the fundamental groups of singular spaces obtained from some finite-volume hyperbolic manifolds by cutting off their cusps and collapsing the resulting boundary tori to points.

Détail

DOI : 10.2140/gt.2020.24.593

Classification : 20F67, 20F65, 57M07
Keywords: hyperbolic group, Gromov boundary

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