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INTRODUCTION WE DEVELOP here a generalization to singular spaces of the Poincare-Lefschetz theory of intersections of homology cycles on manifolds, as announced in [6]. Poincart, in his 1895 paperExpand
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Stratified Morse theory
Suppose that X is a topological space, f is a real valued function on X, and c is a real number. Then we will denote by X ≤c the subspace of points x in X such that f(x)≤c. The fundamental problem ofExpand
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Chern Classes for Singular Algebraic Varieties
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Equivariant cohomology, Koszul duality, and the localization theorem
(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have theExpand
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Intersection homology II
In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is aExpand
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Riemann-roch for singular varieties
The basic tool for a general Riemann-Roch theorem is MacPherson’s graph construction, applied to a complex E. of vector bundles on a scheme Y, exact off a closed subset X. This produces a localizedExpand
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On the Spectrum of the Equivariant Cohomology Ring
Abstract If an algebraic torus $T$ acts on a complex projective algebraic variety $X$ , then the affine scheme $\text{Spec}\,H_{T}^{*}\left( X;\,\mathbb{C} \right)$ associated with the equivariantExpand
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