Exotic structures on quotient spaces ofS3-actions

On exotic algebraic structures on affine spaces

We review the recent developement on the subject, emphasizing its analytic aspects and pointing out some open problems. The study of exotic C-s is at the very beginning, and hopefully this survey would be useful to learn more about these unusual and beautiful objects. All algebraic varieties considered below are usually assumed being smooth, reduced, irreducible, and defined over C. Isomorphism...

LECTURES on EXOTIC ALGEBRAIC STRUCTURES on AFFINE SPACES

These notes are based on the lecture courses given at the Ruhr-Universität-Bochum (03– 08.02.1997) and at the Université Paul Sabatier (Toulouse, 08-12.01.1996).

Exotic projective structures and quasifuchsian spaces II

Let P (S) be the space of projective structures on a closed surface S of genus g > 1 and let Q(S) be the subset of P (S) of projective structures with quasifuchsian holonomy. It is known that Q(S) consists of infinitely many connected components. In this paper, we will show that the closure of any exotic component of Q(S) is not a topological manifold with boundary and that any two components o...

Norms on Quotient Spaces

Exotic smooth structures on nonpositively curved symmetric spaces

We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples are obtained by taking the connected sum with an exotic sphere. To detect the change of the smooth structure we use a tangential map from the locally symmet...