JOURNAL ARTICLE

On the connectedness of the boundary of hierarchically hyperbolic spaces.

  • Published In: Journal of Topology & Analysis, 2026, v. 18, n. 6. P. 1817 1 of 3

  • Database: Mathematics Source 2 of 3

  • Authored By: Tomar, Ravi 3 of 3

Abstract

We prove that, under a mild assumption, any metrizable compactification of a one-ended proper geodesic metric space is connected. As a consequence, we deduce that the boundary, introduced by Durham–Hagen–Sisto, of a one-ended hierarchically hyperbolic space is connected. Moreover, we prove that the connectedness of the boundary of a hierarchically hyperbolic group is equivalent to the one-endedness of the group. As an application, we show that if, for n ≥ 2 , G 1 = A 1 * ⋯ * A n and G 2 = B 1 * ⋯ * B n are free products of one-ended hierarchically hyperbolic groups, then the boundary of G 1 is homeomorphic to the boundary of G 2 if and only if the boundary of A i is homeomorphic to the boundary of B i for 1 ≤ i ≤ n. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Topology & Analysis. 2026/12, Vol. 18, Issue 6, p1817
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2026
  • ISSN:1793-5253
  • DOI:10.1142/S1793525325500323
  • Accession Number:192586411
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