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93
ON RIBBON R 4 ’S
, 1995
"... Abstract. We consider ribbon R 4 ’s, that is, smooth open 4manifolds, homeomorphic to R 4 and associated to hcobordisms between closed 4manifolds. We show that any generalized ribbon R 4 associated to a sequence of hcobordisms between nondiffeomorphic 4manifolds is exotic. Notion of a positive ..."
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Abstract. We consider ribbon R 4 ’s, that is, smooth open 4manifolds, homeomorphic to R 4 and associated to hcobordisms between closed 4manifolds. We show that any generalized ribbon R 4 associated to a sequence of hcobordisms between nondiffeomorphic 4manifolds is exotic. Notion of a
GROMOVWITTEN INVARIANTS OF STABILIZATIONS OF
, 906
"... Abstract. We relate the GromovWitten invariants of X×S 2 to the SeibergWitten invariants of X where X is a simplyconnected symplectic 4manifold. We also give examples that expose the similarity between the classification of smooth 4manifolds and some classification problems regarding symplectic ..."
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symplectic 6manifolds. In this paper, we calculate some of the GromovWitten invariants of the product symplectic structure of X × S 2 where X is a symplectic, simplyconnected 4manifold. X ×S 2 is called the stabilization of X in the sense that when two homeomorphic but nondiffeomorphic 4manifolds
GROMOVWITTEN INVARIANTS OF STABILIZATIONS OF SYMPLECTIC
, 906
"... Abstract. We relate the GromovWitten invariants of X×S 2 to the SeibergWitten invariants of X where X is a simplyconnected symplectic 4manifold. We also give examples that expose the similarity between the classification of smooth 4manifolds and some classification problems regarding symplectic ..."
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symplectic 6manifolds. In this paper, we calculate some of the GromovWitten invariants of the product symplectic structure of X ×S 2 where X is a symplectic, simplyconnected 4manifold. X ×S 2 is called the stabilization of X in the sense that when two homeomorphic but nondiffeomorphic 4manifolds
The varifold representation of nonoriented shapes for diffeomorphic registration
 IN SIAM JOURNAL OF IMAGING SCIENCE
, 2013
"... In this paper, we address the problem of orientation that naturally arises when representing shapes like curves or surfaces as currents. In the field of computational anatomy, the framework of currents has indeed proved very efficient to model a wide variety of shapes. However, in such approaches, ..."
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Cited by 2 (1 self)
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currents require a consistent orientation of all pieces. As a promising alternative to currents, varifolds, introduced in the context of geometric measure theory by F. Almgren, allow the representation of any nonoriented manifold (more generally any nonoriented rectifiable set). In particular, we
On the geography and botany of irreducible 4manifolds with abelian fundamental group
, 2009
"... The geography and botany of smooth/symplectic 4manifolds with cyclic fundamental group are addressed. For all the possible lattice points which correspond to nonspin manifolds of negative signature and a given homeomorphism type, an irreducible symplectic manifold and an infinite family of pairwis ..."
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Cited by 2 (1 self)
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of pairwise nondiffeomorphic nonsymplectic irreducible manifolds are manufactured. In the same fashion, a region of the plane for manifolds with nonnegative signature is filled in.
STEIN 4MANIFOLDS AND CORKS
"... Abstract. It is known that every compact Stein 4manifolds can be embedded into a simply connected, minimal, closed, symplectic 4manifold. Using this property, we give simple constructions of various cork structures of 4manifolds. We also give an example of infinitely many disjoint embeddings of a ..."
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Cited by 2 (1 self)
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of a fixed cork into a noncompact 4manifold which produce infinitely many exotic smooth structures (the authors previously gave examples of arbitrary many disjoint embeddings of different corks in a closed manifold inducing mutually different exotic structures). Furthermore, here we construct
CONSTRUCTING INFINITELY MANY SMOOTH STRUCTURES ON SMALL 4MANIFOLDS
"... The purpose of this article is twofold. First we outline a general construction scheme for producing simply connected minimal symplectic 4manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic 4manifolds homeomorphic but not diffeomorphic ..."
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Cited by 26 (12 self)
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The purpose of this article is twofold. First we outline a general construction scheme for producing simply connected minimal symplectic 4manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic 4manifolds homeomorphic but not diffeomorphic
Nonsingular graphmanifolds of dimension 4
, 2004
"... A compact 4dimensional manifold is a nonsingular graphmanifold if it can be obtained by glueing T 2bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graphstructure is called reduced. We prove th ..."
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Cited by 1 (1 self)
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A compact 4dimensional manifold is a nonsingular graphmanifold if it can be obtained by glueing T 2bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graphstructure is called reduced. We prove
Einstein Metrics and Smooth Structures
 GEOM. TOPOL
, 1998
"... We prove that there are infinitely many pairs of homeomorphic nondiffeomorphic smooth 4manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4manifolds with two smooth structures which admit Einstein metrics with opposi ..."
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Cited by 12 (0 self)
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We prove that there are infinitely many pairs of homeomorphic nondiffeomorphic smooth 4manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4manifolds with two smooth structures which admit Einstein metrics
Einstein metrics and smooth structures
, 1998
"... We prove that there are infinitely many pairs of homeomorphic nondiffeomorphic smooth 4–manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4–manifolds with two smooth structures which admit Einstein metrics with opposi ..."
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We prove that there are infinitely many pairs of homeomorphic nondiffeomorphic smooth 4–manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4–manifolds with two smooth structures which admit Einstein metrics
Results 1  10
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