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56
Gauge theory for embedded surfaces
 I, Topology
, 1993
"... (i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly ..."
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Cited by 68 (6 self)
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(i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly
Selfdual instantons and holomorphic curves
 Annals of Mathematics 139
, 1994
"... 2. Floer homology for symplectic fixed points ..."
Fourmanifold systoles and surjectivity of period map
 Proceedings of conference and workshop in memory of R. Brooks, held at the Technion, Israel Mathematical Conference Proceedings (IMCP), Contemporary
"... Abstract. P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2di ..."
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Cited by 14 (8 self)
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Abstract. P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2dimensional conformal systolic invariant of a 4manifold X with indefinite intersection form. The estimate turns out to be polynomial, rather than logarithmic, in χ(X), if the conjectured surjectivity of the period map is correct. Such surjectivity is targeted by the current work in gauge theory. The surjectivity allows one to insert suitable lattices with metric properties prescribed in advance, into the second de Rham cohomology group of X, as its integer lattice. The idea is to adapt the wellknown Lorentzian construction of the Leech lattice, by replacing the Leech lattice by the ConwayThompson unimodular lattices which define asymptotically dense packings. The final step can be described, in terms of the successive minima λi, as deforming a λ2bound into a λ1bound, illustrated by
Equivariant aspects of YangMills Floer theory
 Topology
"... This paper is concerned with Floer cohomology groups of SO(3) bundles P → Y, where Y is a closed, oriented 3manifold. Following [4] we only ..."
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Cited by 13 (2 self)
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This paper is concerned with Floer cohomology groups of SO(3) bundles P → Y, where Y is a closed, oriented 3manifold. Following [4] we only
Symmetries of the Einstein equations
 Phys. Rev. Lett
, 1993
"... Abstract. We survey recent results and current issues on the existence and uniqueness of Einstein metrics on 4manifolds. A number of open problems and conjectures are presented during the course of the discussion. ..."
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Cited by 12 (2 self)
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Abstract. We survey recent results and current issues on the existence and uniqueness of Einstein metrics on 4manifolds. A number of open problems and conjectures are presented during the course of the discussion.
Nonabelian SeibergWitten theory and stable oriented pairs
 Int. J. Math
"... The aim of this paper is to develop a systematic theory of nonabelian SeibergWitten equations. The equations we introduce and study are associated with a Spin G (4)structure on a 4manifold, where G is a closed subgroup of the ..."
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Cited by 11 (4 self)
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The aim of this paper is to develop a systematic theory of nonabelian SeibergWitten equations. The equations we introduce and study are associated with a Spin G (4)structure on a 4manifold, where G is a closed subgroup of the
Moduli spaces of PU(2)monopoles
 Asian J. Math
"... The most natural way to prove the equivalence between Donaldson theory and SeibergWitten theory is to consider a suitable moduli space of ”nonabelian monopoles”. In [OT5] it was shown that an S 1quotient of a moduli ..."
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Cited by 10 (2 self)
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The most natural way to prove the equivalence between Donaldson theory and SeibergWitten theory is to consider a suitable moduli space of ”nonabelian monopoles”. In [OT5] it was shown that an S 1quotient of a moduli
A survey on Nahm transform
"... We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on R 4 is presented in an uniform manner. We also analyze two new example ..."
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Cited by 9 (3 self)
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We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on R 4 is presented in an uniform manner. We also analyze two new examples, the first of which being the first example involving a fourmanifold that is not hyperk”ahler. 1
Variational aspects of the SeibergWitten functional
 Calc. Var. Partial Diff. Equ
, 1996
"... Recently, Seiberg and Witten (see [SW1], [SW2] and [W]) introduced a new monopole equation which yields new differentialtopological invariants of four dimensional manifolds, closely related to the Donaldson polynomial invarints [DK]. This equation has been used to give more elementary proof of many ..."
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Cited by 9 (1 self)
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Recently, Seiberg and Witten (see [SW1], [SW2] and [W]) introduced a new monopole equation which yields new differentialtopological invariants of four dimensional manifolds, closely related to the Donaldson polynomial invarints [DK]. This equation has been used to give more elementary proof of many heorems in