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

Let Σ be a compact Riemann surface. Any sequence fn : Σ — > M of harmonic maps with bounded energy has a "bubble tree limit" consisting of a harmonic map /o : Σ -> M and a tree of bubbles fk : S2 ->… Expand

We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of… Expand

In the symplectic category there is a 'connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula… Expand

This paper develops the Riemannian geometry of classical gauge theories — Yang-Mills fields coupled with scalar and spinor fields — on compact four-dimensional manifolds. Some important properties of… Expand

This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objects… Expand

The conformal Laplacian D = d*d + (n - 2)s/4(n - 1), acting on functions on a Riemannian manifold Mn with scalar curvature s, is a conformally invariant operator. In this paper we will use D to… Expand