2025/05/07 by Qin Wang, Wang, Qin, Yao, Jvbin
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2505.04118
openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, a notion of the free product X ∗ Y of two metric spaces X and Y has been introduced by T. Fukaya and T. Matsuka. In this paper, we study coarse geometric permanence properties of the free product X ∗ Y. We show that if X and Y satisfy any of the following conditions, then X ∗ Y also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.