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(1.1). This paper concerns three aspects of the action of a compact group K on a space X. The first is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the property that their cohomology may be computed from the structure of the zero and one dimensional orbits of the action of a maximal torus in K. (2) Koszul duality.(More)
Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric(More)
We define an 'enriched' notion of Chow groups for algebraic varieties, agreeing with the conventional notion for complete varieties, but enjoying a func-torial push-forward for arbitrary maps. This tool allows us to glue intersection-theoretic information across elements of a stratification of a variety; we illustrate this operation by giving a direct(More)
Assuming a certain " purity " conjecture, we derive a formula for the (complex) coho-mology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the " kappa " orbital integral that arises in the(More)