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Stable mappings and their singularities
I: Preliminaries on Manifolds.- 1. Manifolds.- 2. Differentiable Mappings and Submanifolds.- 3. Tangent Spaces.- 4. Partitions of Unity.- 5. Vector Bundles.- 6. Integration of Vector Fields.- II:
Symplectic Techniques in Physics
Preface 1. Introduction 2. The geometry of the moment map 3. Motion in a Yang-Mills field and the principle of general covariance 4. Complete integrability 5. Contractions of symplectic homogeneous
The spectrum of positive elliptic operators and periodic bicharacteristics
Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates on
Geometric quantization and multiplicities of group representations
The Heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum-mechanical particle. This can be rephrased as follows: the smallest
Convexity properties of the moment mapping. II
be its associated momen t mapping. (See w for definitions.) The set, @(X), is the union of co-adjoint orbits. The main result of this paper is a description of the orbit structure of this set. To
Symplectic Fibrations And Multiplicity Diagrams
1. Symplectic fibrations 2. Examples of symplectic fibrations: the coadjoint orbit hierarchy 3. Duistermaat-Heckman polynomials 4. Symplectic fibrations and multiplicity diagrams 5. Computations with