Year: 2025
Type: article
Abstract: We study the connection between the fundamental groups of complex hyperbolic manifolds and those of spaces arising from the (relative) strict hyperbolization process due to Charney–Davis and Davis–Januszkiewicz–Weinberger. Viewing a non-uniform lattice Γ in PU ( n , 1 ) \text{PU}(n,1) as a relatively hyperbolic group with respect to its cusp subgroups in the usual way, we show that, when n ≥ 2 n\geq 2 , Γ is not isomorphic to any relatively hyperbolic group arising from the relative strict hyperbolization process, via work of Lafont–Ruffoni. We also prove that a uniform lattice in PU ( n , 1 ) \text{PU}(n,1) is not the fundamental group of a Charney–Davis strict hyperbolization when n ≥ 2 n\geq 2 , assuming the initial complex satisfies some mild conditions.
Source: Journal of Group Theory
Author: Kejia Zhu
Institution: University of California, Riverside
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410765432