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921
Classification of overtwisted contact structures on 3manifolds
 Invent. Math
, 1989
"... We establish a parametric extension hprinciple for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3dimensional result from [7]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of a ..."
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Cited by 181 (1 self)
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We establish a parametric extension hprinciple for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3dimensional result from [7]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class
On the geometric and algebraic rank of graph manifolds
, 2003
"... Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3ngenerated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M is call ..."
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Cited by 16 (1 self)
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is called a Heegaard splitting and denoted by M = V1 ∪S V2. We say that the splitting is of genus g if S is of genus g. It is not difficult to see that any orientable closed 3manifold admits a Heegaard splitting. If M admits a Heegaard splitting of genus g but no Heegaard splitting of smaller genus then we
Improved Localization of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach
 J. Cogn. Neurosci
, 1993
"... We describe a comprehensive linear approach to the prob lem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole st ..."
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Cited by 263 (19 self)
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strengths over the conical surface is highly nnderdetermined, even given closely spaced EEG and MEG recordings. ',x.'c h:,vc obtained much better solutions to this problem by explicitly incorporating both local cortical orientation as well as spatial covariance of sources and sensors into our
Nonorientable 3manifolds admitting coloured triangulations with at most 30 tetrahedra
, 2008
"... We present the census of all nonorientable, closed, connected 3manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid nonbipartite crystallizations up to 30 vertices. ..."
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Cited by 8 (4 self)
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We present the census of all nonorientable, closed, connected 3manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid nonbipartite crystallizations up to 30 vertices.
0Efficient Triangulations of 3Manifolds
 TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
, 2002
"... 0–efficient triangulations of 3–manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3–manifold M can be modified to a 0–efficient triangulation or M can be shown to be one of the manifolds S3, RP3 or L(3, 1). Similarly, any triangulation of a c ..."
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Cited by 75 (15 self)
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0–efficient triangulations of 3–manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3–manifold M can be modified to a 0–efficient triangulation or M can be shown to be one of the manifolds S3, RP3 or L(3, 1). Similarly, any triangulation of a
HOLOMORPHIC DISKS AND THREEMANIFOLD INVARIANTS: PROPERTIES AND APPLICATIONS
, 2001
"... ... and HFred(Y, s) associated to oriented rational homology 3spheres Y and Spin c structures s ∈ Spin c (Y). In the first part of this paper we extend these constructions to all closed, oriented 3manifolds. In the second part, we study the properties of these invariants. The properties include a ..."
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Cited by 201 (31 self)
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... and HFred(Y, s) associated to oriented rational homology 3spheres Y and Spin c structures s ∈ Spin c (Y). In the first part of this paper we extend these constructions to all closed, oriented 3manifolds. In the second part, we study the properties of these invariants. The properties include a
CONTACT CIRCLES ON 3MANIFOLDS
, 1997
"... A contact circle on a 3manifold is a pair of contact forms that defines a linear circle of contact forms (see below for the formal definition). This concept was introduced in [6], and there we gave a complete classification of those 3manifolds that admit a contact circle satisfying a certain addit ..."
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Cited by 9 (3 self)
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additional volume constraint. In the present paper, whose methods are independent of those employed in [6], we show that every (closed, orientable) 3manifold admits a contact circle.
Handlebody construction of Stein surfaces
, 1996
"... The topology of Stein surfaces and contact 3manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained — they correspond to open handlebodies with all handles of index ≤ 2. An uncountable collection of exotic R 4’s is sho ..."
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Cited by 196 (5 self)
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is shown to admit Stein structures. New invariants of contact 3manifolds are produced, including a complete (and computable) set of invariants for determining the homotopy class of a 2plane field on a 3manifold. These invariants are applicable to SeibergWitten theory. Several families of oriented 3
The symplectic nature of fundamental groups of surfaces
 ADV. MATH
, 1984
"... A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures: the ..."
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Cited by 223 (8 self)
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A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures
Results 1  10
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921