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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
K3 surfaces and string duality
"... The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial sp ..."
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Cited by 62 (14 self)
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The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. They also make an almost ubiquitous appearance in the common statements concerning string duality. We review the necessary facts concerning the classical geometry of K3 surfaces that will be needed and then we review “old string theory ” on K3 surfaces in terms of conformal field theory. The type IIA string, the type IIB string, the E8 × E8 heterotic string, and Spin(32)/Z2 heterotic string on a K3 surface are then each analyzed in turn. The discussion is biased in favour of purely geometric notions concerning the K3 surface
String Theory on K3 Surfaces
 Mirror Symmetry II
, 1996
"... The moduli space of N=(4,4) string theories with a K3 target space is determined, establishing in particular that the discrete symmetry group is the full integral orthogonal group of an even unimodular lattice of signature (4,20). The method combines an analysis of the classical theory of K3 moduli ..."
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Cited by 39 (8 self)
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The moduli space of N=(4,4) string theories with a K3 target space is determined, establishing in particular that the discrete symmetry group is the full integral orthogonal group of an even unimodular lattice of signature (4,20). The method combines an analysis of the classical theory of K3 moduli spaces with mirror symmetry. A description of the moduli space is also presented from the viewpoint of quantum geometry, In recent years, CalabiYau manifolds have received great attention in the string literature. This is mainly because compactification on such spaces may be used to reduce the number of dimensions in models built from the intrinsically ten dimensional critical superstring [1]. The focus has largely been on the case of complex dimension d = 3, since the corresponding
FREE CIRCLE ACTIONS WITH CONTRACTIBLE ORBITS ON SYMPLECTIC MANIFOLDS
, 2005
"... ABSTRACT. We prove that closed symplectic fourmanifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do exist, and we give explicit examples based on the ..."
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Cited by 2 (0 self)
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ABSTRACT. We prove that closed symplectic fourmanifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do exist, and we give explicit examples based on the constructions of [5]. 1.