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This volume gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localisation theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.

Cohomology operations. --- Operations (Algebraic topology) --- Algebraic topology --- Algebraic structure. --- Algebraic topology (object). --- Algebraic topology. --- Algebraic variety. --- Basis (linear algebra). --- Boundary (topology). --- CW complex. --- Cellular approximation theorem. --- Characteristic class. --- Classifying space. --- Coefficient. --- Cohomology ring. --- Cohomology. --- Comparison theorem. --- Complex projective space. --- Continuous function. --- Contractible space. --- Cramer's rule. --- Curvature form. --- De Rham cohomology. --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential form. --- Differential geometry. --- Dual basis. --- Equivariant K-theory. --- Equivariant cohomology. --- Equivariant map. --- Euler characteristic. --- Euler class. --- Exponential function. --- Exponential map (Lie theory). --- Exponentiation. --- Exterior algebra. --- Exterior derivative. --- Fiber bundle. --- Fixed point (mathematics). --- Frame bundle. --- Fundamental group. --- Fundamental vector field. --- Group action. --- Group homomorphism. --- Group theory. --- Haar measure. --- Homotopy group. --- Homotopy. --- Hopf fibration. --- Identity element. --- Inclusion map. --- Integral curve. --- Invariant subspace. --- K-theory. --- Lie algebra. --- Lie derivative. --- Lie group action. --- Lie group. --- Lie theory. --- Linear algebra. --- Linear function. --- Local diffeomorphism. --- Manifold. --- Mathematics. --- Matrix group. --- Mayer–Vietoris sequence. --- Module (mathematics). --- Morphism. --- Neighbourhood (mathematics). --- Orthogonal group. --- Oscillatory integral. --- Principal bundle. --- Principal ideal domain. --- Quotient group. --- Quotient space (topology). --- Raoul Bott. --- Representation theory. --- Ring (mathematics). --- Singular homology. --- Spectral sequence. --- Stationary phase approximation. --- Structure constants. --- Sub"ient. --- Subcategory. --- Subgroup. --- Submanifold. --- Submersion (mathematics). --- Symplectic manifold. --- Symplectic vector space. --- Tangent bundle. --- Tangent space. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Unit sphere. --- Unitary group. --- Universal bundle. --- Vector bundle. --- Vector space. --- Weyl group.