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Differential Geometry papers — page 7

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Surgery on Lagrangian and Legendrian Singularities
Let π: E M be a smooth fiber bundle whose total space is a symplectic manifold and whose fibers are Lagrangian. Let L be an embedded Lagrangian submanifold of E. In the paper we address the…
Mikhail EntovJun 5, 1997
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Odd Invariant Semidensity and Divergence-like Operators on an Odd Symplectic Superspace
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant…
O. M. KhudaverdianJun 4, 1997
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The cohomology ring of polygon spaces
We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the…
Jean-Claude Hausmann, Allen KnutsonJun 1, 1997
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Extensions of Lie-Rinehart algebras and the Chern-Weil construction
A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for…
Johannes HuebschmannJun 1, 1997
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An Obstruction to Quantizing Compact Symplectic Manifolds
We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the…
Mark J. Gotay, Janusz Grabowski, Hendrik B. GrundlingMay 31, 1997
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Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold
We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4-manifolds, and use it to classify local forms on neighborhoods of singular circles on which the 2-form vanishes. Removing…
Ko HondaMay 30, 1997
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Surfaces in 4-Manifolds
In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold…
Ronald Fintushel, Ronald J. SternMay 29, 1997
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Quantization of Presymplectic Manifolds and Circle Actions
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a…
Ana Canas da Silva, Yael Karshon, Susan TolmanMay 17, 1997
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On the Scalar Curvature of Einstein Manifolds
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture…
Fabrizio Catanese, Claude LeBrunMay 14, 1997
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An Extension of the Work of V. Guillemin on Complex Powers and Zeta Functions of Elliptic Pseudodifferential Operators
The purpose of this note is to extend the results of V. Guillemin on elliptic self-adjoint pseudodifferential operators of order one, from operators defined on smooth functions on a closed manifold…
Bogdan BucicovschiMay 9, 1997
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Semidirect products and the Pukanszky condition
We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction…
P. BaguisMay 5, 1997
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Invariants in c U p-Geometry
This note describes the construction of c U p-invariant differential operators on statistical manifolds, i.e. of operators canonically associated to a geometry which synthetizes the properties of…
G. BurdetMay 5, 1997
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Symplectic aspects of the first eigenvalue
There are two themes in the present paper. The first one is spelled out in the title, and is inspired by an attempt to find an analogue of Hersch-Yang-Yau estimate for lambda1 of surfaces in…
Leonid PolterovichMay 4, 1997
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Holomorphic Morse Inequalities and Symplectic Reduction
We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights…
Maxim BravermanMay 2, 1997
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Uniformization of four manifolds
We characteristize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten…
Naichung Conan LeungMay 2, 1997
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A Schlafli-type formula for convex cores of hyperbolic 3-manifolds
In 3-dimensional hyperbolic geometry, the classical Schlafli formula expresses the variation of the volume of a hyperbolic polyhedron in terms of the length of its edges and of the variation of its…
Francis BonahonApr 30, 1997
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Variations of the boundary geometry of 3--dimensional hyperbolic convex cores
A fundamental object in a hyperbolic 3-manifold M is its convex core C(M), defined as the smallest closed non-empty convex subset of M. We investigate the way the geometry of the boundary S of C(M)…
Francis BonahonApr 30, 1997
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Bounded and L2 Harmonic Forms on Universal Covers
We relate the positivity of the curvature term in the Weitzenbock formula for the Laplacian on p-forms on a complete manifold to the existence of bounded and L2 harmonic forms. In the case where…
K. D. Elworthy, Xue-Mei Li, Steven RosenbergApr 25, 1997
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Radiation structures on isotropic hypersurfaces
The geometrical structures (in the sense of E. Cartan) are analyzed which underlie the gravitational radiation phenomenon. Among the results are : - the introduction of the adapted frame bundle to a…
G. Burdet, M. PerrinApr 25, 1997
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Chaotic Geodesics in Carnot Groups
The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the…
R. Montgomery, M. Shapiro, A. StolinApr 25, 1997
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Deformations of Nonholonomic Two-plane Fields in Four Dimensions
An Engel structure is a maximally non-integrable field of two-planes tangent to a four-manifold. Any two such structures are locally diffeomorphic. We investigate the space of global deformations of…
Richard MontgomeryApr 25, 1997
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Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
We show that most homogeneous Anosov actions of higher rank Abelian groups are locally smoothly rigid (up to an automorphism). This result is the main part in the proof of local smooth rigidity for…
A. Katok, R. J. SpatzierApr 24, 1997
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Seiberg-Witten Theory and Z/2p actions on spin 4-manifolds
Furuta's ``10/8-th's'' theorem gives a bound on the magnitude of the signature of a smooth spin 4-manifold in terms of the second Betti number. We show that in the presence of a Z/2p…
Jim BryanApr 22, 1997
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Rozansky-Witten invariants via formal geometry
We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from…
M. KontsevichApr 19, 1997
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A-hat Genus and Collapsing
We give relationships between the vanishing of the A-hat genus and the possibility that a spin manifold can collapse with curvature bounded below.
John LottApr 17, 1997
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