New hyperbolic 4–manifolds of low volume

Riolo, Stefano; Slavich, Leone

doi:10.2140/agt.2019.19.2653

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New hyperbolic $4$–manifolds of low volume

Stefano Riolo and Leone Slavich

Algebraic & Geometric Topology 19 (2019) 2653–2676

DOI: 10.2140/agt.2019.19.2653

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

Volume 19, issue 5 (2019)