Generalized symplectic rational blowdowns

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.Comment: Version 2: Correction of a minor error pointed out by an anonymous referee, correction of typos and improvement of exposition. Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-26.abs.htm

Symplectic rational blowdowns

We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic $K3$ surfaces of Gompf and Mrowka, admit symplectic structures.Comment: 12 pages; 4 figures; Latex2e documen

Metaphysics Renewed: Kant’s Schematized Categories and the Possibility of Metaphysics

This article considers the significance of Kant’s schematized categories in the Critique of Pure Reason for contemporary metaphysics. I present Kant’s understanding of the schematism and how it functions within his critique of the limits of pure reason. Then I argue that, although the true role of the schemata is a relatively late development in Kant’s thought, it is nevertheless a core notion, and the central task of the first Critique can be sufficiently articulated in the language of the schematism. A surprising result of Kant’s doctrine of the schematism is that a limited form of metaphysics is possible even within the parameters set out in the first Critique. To show this, I offer contrasting examples of legitimate and illegitimate forays into metaphysics in light of the condition of the schematized categories

A new symplectic surgery: the 3-fold sum

AbstractWe define a symplectic surgery along positively intersecting symplectic surfaces in 4-manifolds, the generalized symplectic sum, and prove an existence theorem for the special case of a 3-fold sum. With a slight generalization of the 3-fold sum, we show how to sum along immersed surfaces and indicate a relation between the sums and algebraic desingularization. We use images of the moment map for a torus acting in the neighborhood of intersection points to illustrate when it is possible to perform the proposed sums