Hisaaki Endo (Tokyo Institute of Technology)

Inoue surfaces and their generalizations

Abstract

We give a new generalization of famous Inoue's surfaces to higher dimensions. Let M be a matrix in SL(2n+1,Z) having only one real eigenvalue which is simple. We associate to M a complex manifold of complex dimension n+1. This manifold fibers over the circle with fiber a (2n+1)-dimensional torus and monodromy the transpose of M. Our construction is elementary and does not use algebraic number theory. We show that some of the Oeljeklaus-Toma manifolds are biholomorphic to manifolds of this type. We prove that if M is not diagonalizable, then the manifold does not admit a Kahler structure and is not homeomorphic to any of Oeljeklaus-Toma manifolds. This is a joint work with Andrei Pajitnov.