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Riemannian hyperbolization

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Abstract

The strict hyperbolization process of Charney and Davis produces a large and rich class of negatively curved spaces (in the geodesic sense). This process is based on an earlier version introduced by Gromov and later studied by Davis and Januszkiewicz. If M is a manifold its Charney-Davis strict hyperbolization is also a manifold, but the negatively curved metric obtained is very far from being Riemannian because it has a large and complicated set of singularities. We show that these singularities can be removed (provided the hyperolization piece is large). Hence the strict hyperbolization process can be done in the Riemannian setting.

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Authors and Affiliations

  1. SUNY, Binghamton, NY, 13902, USA

    Pedro Ontaneda

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  1. Pedro Ontaneda
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Correspondence to Pedro Ontaneda.

Additional information

Pedro Ontaneda was partially supported by a NSF grant.

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Ontaneda, P. Riemannian hyperbolization. Publ.math.IHES 131, 1–72 (2020). https://doi.org/10.1007/s10240-020-00113-1

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  • DOI: https://doi.org/10.1007/s10240-020-00113-1

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