Topologische Eigenschaften von Kompaktifizierungen glatter offener Mannigfaltigkeiten
Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms , when k >1. Classical theory describes U(f) as the complement in of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on , we give a definition of linking number between closed loops in and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in . As an application, we use these linking...
A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of...
In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name