Exotic structures and the limitations of certain analytic methods in geometry (Q2484135)

In this paper, dedicated to the memory of Armand Borel, the authors ``review some results concerning negatively curved exotic structures (DIFF and PL) and its (unexpected) implications on the limitations of some analytic methods in geometry''. The paper represents a very good survey of results on this subject. They include not only the famous examples of nondiffeomorphic homeomorphic Riemannian manifolds with all sectional curvatures in the interval \((-1-\varepsilon,-1+\varepsilon)\) where \(\varepsilon\) can be any positive number (Farrel-Jones) and of a diffeomorphism \(f\) between a pair of closed negatively curved Riemannian manifolds such that the unique harmonic map homotopic to \(f\) is not one-to-one (Farrell-Ontaneda-Raghunathan) but also recent examples of negatively curved manifolds for which the Ricci flow does not converge smoothly (Farrell-Ontaneda).