Negatively curved Einstein metrics on Gromov-Thurston manifolds

Abstract

For every $n\ge 4$ we construct infinitely many mutually not homotopic closed manifolds of dimension $n$ which admit a negatively curved Einstein metric but no locally symmetric metric.

arXiv comment29 pages, 1 figure. Version 2: Minor corrections in Sections 1-4, and Section 5 was rewritten for forthcoming work