LECTURES ON LOCALIZATION AND EQUIVARIANT COHOMOLOGY

                                                         1.  Fiber Integration, Poincaré Duals and Thom Classes

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                                                2.  Duistermaat-Heckman Theorem and Exact Stationary Phase Approximation

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                                                3.  Generalized Duistermaat-Heckman Theorem

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                                                4.  Generalized Duistermaat-Heckman Implies Duistermaat-Heckman

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                                                5.  Equivariant  Cohomology and Localization (Isolated Zeros)

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                                               6.  Equivariant Localization Implies Generalized Duistermaat-Heckman

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                                               7.  Proof of Equivariant Localization (Isolated Zeros)

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                                               8.  Discrete S¹-Localization and the Equivariant Euler Class

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                                               9.   REFERENCES