Hyperbolic manifolds with negatively curved exotic triangulations in dimension six (Q1336252)

Given \(\varepsilon > 0\), the author constructs closed real hyperbolic manifolds of dimension 6 with exotic triangulations admitting Riemannian metrics with sectional curvatures in the interval \((-1 - \varepsilon, -1 + \varepsilon)\). The idea of the paper is the following: triangulations are changed by cutting along a hypersurface and glueing back with a twist. This surface is considered to be totally geodesic and the author finds one with a large tubular neighbourhood width so that he can provide this triangulation with a Riemannian metric the sectional curvature of which is in the interval \((-1 - \varepsilon, -1 + \varepsilon)\).