arXiv subjects
Publications and source records attributed to Stefano Vidussi.
This short note presents a simple construction of nonisotopic symplectic tori representing the same primitive homology class in the symplectic 4-manifold E(1)_K, obtained by knot surgery on the rational elliptic surface E(1) with the left-handed trefoil knot K. E(1)_K has the simplest homotopy type among simply-connected symplectic 4-manifolds known to exhibit such property.
The aim of this paper is to discuss some applications of the relation between Seiberg-Witten theory and two natural norms defined on the first cohomology group of a closed 3-manifold N - the Alexander and Thurston norms. We start by giving a "new" proof of McMullen's inequality between these norms, and then use these norms to study two problems related to symplectic 4-manifolds of the form S^1xN. First we prove that - as long as N is irreducible - the unit balls of these norms are related in a way similar to the case of fibered 3-manifolds, supporting the conjecture that N is fibered. Second, we provide the first example of a 2-cohomology class on a symplectic manifold that lies in the positive cone and satisfies Taubes' "more constraints", but cannot be represented by a symplectic form.
In this note we present a new definition of the 4-manifold admitting inequivalent symplectic structures constructed by McMullen-Taubes which leads to the identification of a new symplectic structure. We prove moreover that it is diffeomorphic to one of the link surgery manifolds introduced by Fintushel-Stern.
In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent symplectic structures Keywords: Symplectic topology of 4-manifolds; Seiberg-Witten theory