(Note: There are no symplectic forms on X unless b and the first Betti number of X have opposite parity.) In a subsequent article with joint authors, a vanishing theorem will be proved for the… Expand

This note describes a subcomplex F of the de Rham complex of parametrized knot space, which is combinatorial over a number of universal ‘‘Anomaly Integrals.’’ The self‐linking integrals of… Expand

The purpose of this article is to explain how pseudo-holomorphic curves in a symplectic 4-manifold can be constructed from solutions to the Seiberg-Witten equations. As such, the main theorem proved… Expand

This paper gives a mathematically rigorous proof of the positive energy theorem using spinors. This completes and simplifies the original argument presented by Edward Witten. We clarify the geometric… Expand

Using a mathematical model for the regulation of gene expression, the conditions under which cis-trans compensatory evolution can lead to misexpression in interspecific hybrids are explored and 13 candidate genes whose dysregulation might be the consequence of coevolution of cis- and trans-regulatory elements within species are found.Expand

1. SW => Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves 1. The Seiberg-Witten equations 2. Estimates 3. The monotonicity formula 4. The local structure of [alpha]1(0) 5.… Expand