Applications of Equivariant Cohomology

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Applications of Equivariant Cohomology
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We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular, we state a conjecture for the index of a transversally elliptic operator linked to a Hamiltonian action. In the last part, we describe algorithms for numerical computations of values of multivariate spline functions and of vector-partition functions of classical root systems.
Keywords equivariant cohomology Hamiltonian action symplectic reduction localization formula polytope index transversally elliptic operator spline Euler–Maclaurin formula
Group representation Mathematics Group action Process (computing) Stagnation point Euler angles Cuboid
Presentation of a group Process (computing) Multiplication sign Conservation law Summierbarkeit
Group action Symmetry (physics) Order (biology) Musical ensemble
Point (geometry) Addition Military base Multiplication sign Thermal expansion Functional (mathematics) Grothendieck topology Numerical analysis Arithmetic mean Geometric quantization Spring (hydrology) Voting Vector space Network topology Series (mathematics) Coefficient Fundamental theorem of algebra
Group action Presentation of a group Limit of a sequence Water vapor Open set Dimensional analysis Explosion Fraction (mathematics) Sign (mathematics) Roundness (object) Different (Kate Ryan album) Physical system Potenz <Mathematik> Sampling (statistics) Lattice (order) Arithmetic mean Order (biology) Phase transition Summierbarkeit Figurate number Directed graph Spacetime Point (geometry) Beat (acoustics) Partition function (statistical mechanics) Student's t-test Rule of inference Continuous function Event horizon Scheduling (computing) Frequency Goodness of fit Helmholtz decomposition Modulform Nichtlineares Gleichungssystem Focus (optics) Distribution (mathematics) Matching (graph theory) Weight Model theory Physical law Algebraic structure Basis <Mathematik> Volume (thermodynamics) Theory of everything Musical ensemble Game theory Table (information) Building INTEGRAL State of matter Multiplication sign Direction (geometry) Parameter (computer programming) Mereology Food energy Grothendieck topology Subset Mathematics Coefficient of determination Many-sorted logic Oval Square number Cuboid Extension (kinesiology) Differential topology Partition (number theory) Fiber (mathematics) Process (computing) Mass flow rate Closed set Moment (mathematics) Thermal expansion Price index Functional (mathematics) Measurement Curvature Shooting method Right angle Ocean current Geometry Cue sports Functional (mathematics) Flock (web browser) Divisor Population density Causality Average Operator (mathematics) Euklidischer Ring Addition Time zone Dependent and independent variables Military base Forcing (mathematics) Projective plane Numerical analysis Voting Object (grammar) Maß <Mathematik>
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