| Abstract: |
| We construct Einstein metrics of negative sectional curvature on ramified covers of compact hyperbolic four-manifolds with symmetries, initially considered by Gromov and
Thurston. These metrics are obtained through a deformation procedure.
The approximate Einstein metric is an interpolation between a
black-hole Einstein metric near the branch locus and the
pulled-back hyperbolic metric. The deformation relies on an involved
bootstrap procedure. Our construction yields the first example of
compact Einstein manifolds with negative sectional curvature which are
not locally homogeneous. |
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