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New hyperbolic $4$–manifolds of low volume

Stefano Riolo and Leone Slavich

Algebraic & Geometric Topology 19 (2019) 2653–2676
Abstract

We prove that there are at least two commensurability classes of (cusped, arithmetic) minimal-volume hyperbolic 4–manifolds. Moreover, by applying a well-known technique due to Gromov and Piatetski-Shapiro, we build the smallest known nonarithmetic hyperbolic 4–manifold.

Keywords
hyperbolic $4$–manifold, minimal-volume hyperbolic manifolds
Mathematical Subject Classification 2010
Primary: 57M50, 57N16
References
Publication
Received: 8 August 2018
Revised: 19 October 2018
Accepted: 30 October 2018
Published: 20 October 2019
Authors
Stefano Riolo
Institut de mathématiques
University of Neuchâtel
Neuchâtel
Switzerland
Leone Slavich
Department of Mathematics
University of Pisa
Pisa
Italy