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Convex polytopes --- Symplectic manifolds

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The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal.

Cosmology --- Geometry, Differential. --- Lorentz transformations. --- Mathematical models. --- Automorphism. --- Bijection. --- C0. --- Canonical form. --- Canonical transformation. --- Cauchy distribution. --- Causal structure. --- Cayley transform. --- Codimension. --- Cohomology. --- Cokernel. --- Compactification (mathematics). --- Complexification (Lie group). --- Computation. --- Conformal geometry. --- Conformal map. --- Conformal symmetry. --- Connected sum. --- Contact geometry. --- Corank. --- Covariant derivative. --- Covering space. --- Deformation theory. --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential operator. --- Dimension (vector space). --- Einstein field equations. --- Equation. --- Euler characteristic. --- Existential quantification. --- Fiber bundle. --- Fibration. --- Floquet theory. --- Four-dimensional space. --- Fourier integral operator. --- Fourier transform. --- Fundamental group. --- Geodesic. --- Hamilton–Jacobi equation. --- Hilbert space. --- Holomorphic function. --- Holomorphic vector bundle. --- Hyperfunction. --- Hypersurface. --- Integral curve. --- Integral geometry. --- Integral transform. --- Intersection (set theory). --- Invertible matrix. --- K-finite. --- Lagrangian (field theory). --- Lie algebra. --- Light cone. --- Linear map. --- Manifold. --- Maxima and minima. --- Minkowski space. --- Module (mathematics). --- Notation. --- One-parameter group. --- Parametrix. --- Parametrization. --- Principal bundle. --- Product metric. --- Pseudo-differential operator. --- Quadratic equation. --- Quadratic form. --- Quadric. --- Radon transform. --- Riemann surface. --- Riemannian manifold. --- Seifert fiber space. --- Sheaf (mathematics). --- Siegel domain. --- Simply connected space. --- Submanifold. --- Submersion (mathematics). --- Support (mathematics). --- Surjective function. --- Symplectic manifold. --- Symplectic vector space. --- Symplectomorphism. --- Tangent space. --- Tautology (logic). --- Tensor product. --- Theorem. --- Topological space. --- Topology. --- Two-dimensional space. --- Unit vector. --- Universal enveloping algebra. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Vector space. --- Verma module. --- Volume form. --- X-ray transform.

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Differential topology --- 515.16 --- Geometry, Differential --- Topology --- Topology of manifolds --- Differential topology. --- 515.16 Topology of manifolds --- Topologie differentielle

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"The first half of this monograph ... is basically an exegesis of Cartan's two seminal papers from 1950 on equivariant de Rham theory. In the second half we'll discuss a few of the post-1950 developments in this area."

Homology theory. --- Supersymmetry. --- Homologie --- Supersymétrie --- 512.8 --- Lie groups, Lie algebras --- Supersymétrie --- Homology theory --- Supersymmetry --- Unified theories --- Particles (Nuclear physics) --- Symmetry (Physics) --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Cartan, Henri --- Algebraic topology. --- Differential geometry. --- Mathematical physics. --- Algebraic Topology. --- Differential Geometry. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Differential geometry --- Topology --- Mathematics --- Cartan, Henri, --- Analyse sur une variété --- Formes differentielles --- Topologie algebrique --- Homologie et cohomologie