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Differential Geometry papers — page 3

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Ring structure of the Floer Cohomology of Σ× S1
We give a presentation for the Floer cohomology ring HF*(Σ× S1), where Σ is a Riemann surface of genus bigger than one, which coincides with the conjectural presentation for the quantum…
Vicente MuñozOct 27, 1997
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Surfaces in Lie sphere geometry and the stationary Davey-Stewartson hierarchy
We introduce two basic invariant forms which define generic surface in 3-space uniquely up to Lie sphere equivalence. Two particularly interesting classes of surfaces associated with these invariants…
E. V. FerapontovOct 27, 1997
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Generalized Symplectic Manifolds
This paper uses a generalization of symplectic geometry, known as n-symplectic geometry and developed by Norris, to find observables on three-dimensional manifolds. It will be seen that for the…
Daniel CartinOct 24, 1997
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Introduction to the Tangent Grupoid
We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.
Alejandro RiveroOct 23, 1997
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Intersection Cohomology of Symplectic Quotients
Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!
Jonathan WoolfOct 23, 1997
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Topology of solutions of the Liouville equation
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
Wlodzimierz PiechockiOct 22, 1997
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Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold
We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Consequently…
Mark J. Gotay, Hendrik B. GrundlingOct 22, 1997
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Analytic Torsion for Quaternionic manifolds and related topics
In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds…
Naichung Conan Leung, Sangkug YiOct 21, 1997
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Topology of the set of smooth solutions to the Liouville equation
We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic.
Kazimierz Bragiel, Wlodzimierz PiechockiOct 21, 1997
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Cap-prodcut structures on the Fintushel-Stern spectral sequence
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the 8-graded instanton Floer…
Weiping LiOct 20, 1997
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Three Cocycles on (S1) Generalizing the Schwarzian Derivative
The first group of differentiable cohomology of (S1), vanishing on the Möbius subgroup PSL(2,R)⊂(S1), with coefficients in modules of linear differential operators on S1 is…
S. Bouarroudj, V. OvsienkoOct 18, 1997
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Topological rigidity of Hamiltonian loops and quantum homology
This paper studies the question of when a loop ϕ in the group Symp(M,ω) of symplectomorphisms of a symplectic manifold (M,ω) is isotopic to a loop that is generated by a time-dependent…
François Lalonde, Dusa McDuff, Leonid PolterovichOct 17, 1997
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A new flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications
Using the Bryant representation, we define a new flux on homology classes of CMC-1 surfaces in hyperbolic 3-space, satisfying a balancing formula which is useful to show nonexistencd of certain kinds…
Wayne Rossman, Masaaki Umehara, Kotaro YamadaOct 17, 1997
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Double vector bundles and duality
The most important examples of a double vector bundle are provided by iterated tangent and cotangent functors: TTM, TT*M, T*TM, and T*T*M. We introduce the notions of the dual double vector…
Katarzyna Konieczna, Pawel UrbanskiOct 16, 1997
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Mathematical Background of Formalism of Operator Manifold
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate…
G. T. Ter-KazarianOct 16, 1997
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Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids
Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed…
Janusz Grabowski, Pawel UrbanskiOct 14, 1997
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Uhlenbeck compactness and transversality for the moduli space of PU(2) monopoles
This research announcement gives a brief report of the main results in our paper "PU(2) monopoles, I: Regularity, Uhlenbeck compactness, and transversality" (Journal of Differential Geometry,…
Paul M. N. Feehan, Thomas G. LenessOct 12, 1997
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Cocycles, symplectic structures and intersection
We investigate the cross ratio for closed negatively curved manifolds. As one of several applications, we obtain that for two such homotopy equivalent manifolds M and N, the following is true : If M…
Ursula HamenstaedtOct 9, 1997
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Deficiencies of Lattice Subgroups of Lie Groups
Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.
John LottOct 9, 1997
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Lie algebroids and Poisson-Nijenhuis structures
Poisson-NIjenhuis structures for an arbitrary Lie agebroid are defined and studied by means of tangent lifts of tensor fields.
Janusz Grabowski, Pawel UrbanskiOct 7, 1997
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An analysis of the two-vortex case in the Chern-Simons Higgs model
Extending work of Caffarelli-Yang and Tarantello, we present a variational existence proof for two-vortex solutions of the periodic Chern-Simons Higgs model and analyze the asymptotic behavior of…
W. Ding, J. Jost, J. Li et al.Oct 7, 1997
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The differential equation Δu = 8π- 8πh u on a compact Riemann surface
Let M be a compact Riemann surface, h(x) a positive smooth function on M. In this paper, we consider the functional J(u)=1/2∫ M| u| 2 + 8π∫Mu…
W. Ding, J. Jost, J. Li et al.Oct 7, 1997
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Isospectral deformations of closed Riemannian manifolds with different scalar curvature
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on Sn× Tm, where Tm is a torus…
Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth et al.Oct 6, 1997
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Non-Symplectic Geometry of First Order Time-Dependent Mechanics
The usual formulation of time-dependent mechanics implies a given splitting Y=R× M of an event space Y. This splitting, however, is broken by any time-dependent transformation, including…
G. SardanashvilyOct 4, 1997
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Residual Amenability and the Approximation of L2-invariants
We generalize Luck's Theorem to show that the L2-Betti numbers of a residually amenable covering space are the limit of the L2-Betti numbers of a sequence of amenable covering spaces. We show…
Bryan ClairOct 3, 1997
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