Journal of the Ramanujan Mathematical Society

Volume 40, Issue 3, September 2025 pp. 269–331.

A combination theorem for trees of metric bundles

Authors: Rakesh Halder
Author institution:Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector~81, S.A.S. Nagar~140~306, Punjab, India.

Summary: Motivated by the work of Bestvina–Feighn ([BF92]) and Mj–Sardar ([MS12]), we define trees of metric bundles subsuming both the trees of metric spaces and the metric bundles. Then we prove a combination theorem for these spaces. More precisely, we prove that the total space of a tree of metric bundles is hyperbolic if the following hold (see Theorem 1.5). (1) The fibers are uniformly hyperbolic metric spaces and the base is also hyperbolic metric space, (2) barycenter maps for the fibers are uniformly coarsely surjective, (3) the edge spaces are uniformly qi embedded in the corresponding fibers and (4) the Bestvina–Feighn hallway flaring condition is satisfied. As an application, we provide a combination theorem for certain complexes of groups over finite simplicial complex (see Theorem 1.3).

Contents Full-Text PDF