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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:Expand
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 homogeneousExpand
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 onExpand
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 smallestExpand
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. ToExpand
Supersymmetry and equivariant de Rham theory
1 Equivariant Cohomology in Topology.- 3 The Weil Algebra.- 4 The Weil Model and the Cartan Model.- 5 Cartan's Formula.- 6 Spectral Sequences.- 7 Fermionic Integration.- 8 Characteristic Classes.- 9Expand
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 withExpand
A New Proof of Weyl's Formula on the Asymptotic Distribution of Eigenvalues
One of the more perplexing problems of finite particle quantum mechanics is to find the appropriate quantum mechanical description of a given classical mechanical system. Unfortunately, from theExpand