Volume 19, issue 5 (2019)

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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