Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures

We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold. We give applications to computing Seiberg-Witten invariants of four-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities previously obtained by Oszv\'ath and Szab\'o.Comment: 26 pages, no figures, Latex2e, to appear in Math. Nac

Integrated management of hierarchical levels: towards a CAPE tool

The integration of decision-making procedures usually assigned to different hierarchical production systems requires the use of complex mathematical models and high computational efforts, in addition to the need of an extensive management of data and knowledge within the production systems. This work addresses this integration problem and proposes a comprehensive solution approach, as well as guidelines for Computer Aided Process Engineering (CAPE) tools managing the corresponding cyberinfrastructure. This study presents a methodology based on a domain ontology which is used as the connector between the introduced data, the different available formulations developed to solve the decision-making problem, and the necessary information to build the finally required problem instance. The methodology has demonstrated its capability to help exploiting different available decision-making problem formulations in complex cases, leading to new applications and/or extensions of these available formulations in a robust and flexible way.Peer ReviewedPostprint (author's final draft

Spin(7)-instantons, stable bundles and the Bogomolov inequality for complex 4-tori

Using gauge theory for Spin(7)-manifolds of dimension 8, we develop a procedure, called Spin-rotation, which transforms a (stable) holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new holomorphic structure over a different complex torus. We show non-trivial examples of this procedure by rotating a decomposable Weil abelian variety into a non-decomposable one. As a byproduct, we obtain a Bogomolov type inequality, which gives restrictions for the existence of stable bundles on an abelian variety of dimension 4, and show examples in which this is stronger than the usual Bogomolov inequality.Comment: 40 pages, no figures; v2. To appear in Journal de math\'ematiques pures et appliqu\'ee

The Rejection of Consequentializing

Consequentialists say we may always promote the good. Deontologists object: not if that means killing one to save five. “Consequentializers” reply: this act is wrong, but it is not for the best, since killing is worse than letting die. I argue that this reply undercuts the “compellingness” of consequentialism, which comes from an outcome-based view of action that collapses the distinction between killing and letting die