Trees of metric compacta and trees of manifolds

Świątkowski, Jacek¹

¹ Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland

Geometry & topology, Tome 24 (2020) no. 2, pp. 533-592.

Résumé

We present a construction, called a tree of spaces, that allows us to produce many compact metric spaces that are good candidates for being (up to homeomorphism) Gromov boundaries of some hyperbolic groups. We develop also a technique that allows us (1) to work effectively with the spaces in this class and (2) to recognize ideal boundaries of various classes of infinite groups, up to homeomorphism, as some spaces in this class.

We illustrate the effectiveness of the presented technique by clarifying, correcting and extending various results concerning the already widely studied class of spaces called trees of manifolds.

In a companion paper (Geom. Topol. 24 (2020) 593–622), which builds upon results from the present paper, we show that trees of manifolds in arbitrary dimension appear as Gromov boundaries of some hyperbolic groups.

Détail

DOI : 10.2140/gt.2020.24.533

Classification : 20F65, 57M07, 54D80
Keywords: compact metric space, inverse limit, ideal boundary

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