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47
Supersymmetric Yang–Mills theory on a fourmanifold
 Jour. Math. Phys
, 1994
"... By exploiting standard facts about N = 1 and N = 2 supersymmetric YangMills theory, the Donaldson invariants of fourmanifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about ..."
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Cited by 67 (4 self)
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By exploiting standard facts about N = 1 and N = 2 supersymmetric YangMills theory, the Donaldson invariants of fourmanifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric YangMills theory. In fourdimensional supersymmetric YangMills theory formulated on flat R4, certain correlation functions are independent of spatial separation and are hence effectively computable by going to short distances. This is the basis for one of the most fruitful techniques for studying dynamics of those theories [1,2], and
Monopoles and four manifolds
 Math.Res. Lett
, 1994
"... Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by ..."
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Cited by 67 (2 self)
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Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by counting solutions of a nonlinear equation with an abelian gauge group. This is a “dual ” equation in which the gauge group is the dual of the maximal torus of SU(2). The new viewpoint suggests many new results about the Donaldson invariants. November
INTEGRATION OVER THE uPLANE IN DONALDSON THEORY
, 1997
"... We analyze the uplane contribution to Donaldson invariants of a fourmanifold X. For b + 2(X)> 1, this contribution vanishes, but for b + 2 =1, the Donaldson invariants must be written as the sum of a uplane integral and an SW contribution. The uplane integrals are quite intricate, but can be anal ..."
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Cited by 52 (2 self)
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We analyze the uplane contribution to Donaldson invariants of a fourmanifold X. For b + 2(X)> 1, this contribution vanishes, but for b + 2 =1, the Donaldson invariants must be written as the sum of a uplane integral and an SW contribution. The uplane integrals are quite intricate, but can be analyzed in great detail and even calculated. By analyzing the uplane integrals, the relation of Donaldson theory to N = 2 supersymmetric YangMills theory can be described much more fully, the relation of Donaldson invariants to SW theory can be generalized to fourmanifolds not of simple type, and interesting formulas can be obtained for the class numbers of imaginary quadratic fields. We also show how the results generalize to extensions of Donaldson theory obtained by including hypermultiplet matter fields.
Categorical Construction of 4D Topological Quantum Field Theories
 in Quantum Topology, L.H. Kauffman and R.A. Baadhio, eds., World Scientific
, 1993
"... In recent years, it has been discovered that invariants of three dimensional ..."
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Cited by 50 (7 self)
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In recent years, it has been discovered that invariants of three dimensional
Holomorphic triangle invariants and the topology of symplectic fourmanifolds
 Duke Math. J
"... This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth fourmanifolds constructed using holomorphic triangles introduced in [20]. Specifically, we establish a nonvanishing result for the invariants of symplectic fourmanifolds, which leads to new ..."
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Cited by 35 (5 self)
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This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth fourmanifolds constructed using holomorphic triangles introduced in [20]. Specifically, we establish a nonvanishing result for the invariants of symplectic fourmanifolds, which leads to new proofs of the indecomposability theorem for symplectic fourmanifolds and the symplectic Thom conjecture. As a new application, we generalize the indecomposability theorem to splittings of fourmanifolds along a certain class of threemanifolds obtained by plumbings of spheres. This leads to restrictions on the topology of Stein fillings of such threemanifolds.
Vector bundles and SO(3)invariants for elliptic surfaces
 J. Amer. Math. Soc
, 1995
"... Let S be a simply connected elliptic surface with at most two multiple fibers. In this paper, the second in a series of three, we are concerned with describing moduli spaces of stable vector bundles V over S such that the restriction of c1(V) to a ..."
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Cited by 23 (3 self)
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Let S be a simply connected elliptic surface with at most two multiple fibers. In this paper, the second in a series of three, we are concerned with describing moduli spaces of stable vector bundles V over S such that the restriction of c1(V) to a
Exotic smooth structures on small 4Manifolds
, 2007
"... Dedicated to Ronald J. Stern on the occasion of his sixtieth birthday Abstract. Let M be either CP 2 #3CP 2 or 3CP 2 #5CP 2. We construct the first example of a simplyconnected irreducible symplectic 4manifold that is homeomorphic but not diffeomorphic to M. 1. ..."
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Cited by 17 (6 self)
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Dedicated to Ronald J. Stern on the occasion of his sixtieth birthday Abstract. Let M be either CP 2 #3CP 2 or 3CP 2 #5CP 2. We construct the first example of a simplyconnected irreducible symplectic 4manifold that is homeomorphic but not diffeomorphic to M. 1.
A symplectic manifold homeomorphic but not diffeomorphic to
 CP2 # 3CP2
"... Abstract. In this paper we construct a minimal symplectic 4manifold and prove it is homeomorphic but not diffeomorphic to CP 2 #3CP 2. 1. ..."
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Cited by 12 (1 self)
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Abstract. In this paper we construct a minimal symplectic 4manifold and prove it is homeomorphic but not diffeomorphic to CP 2 #3CP 2. 1.