Abstract
INTRODUCTION A p-torus is a product of cyclic groups of order p if p is an odd prime, and a product of circles if p is zero. In this paper we are concerned with the smooth action of a p-torus A on a differentiable manifold M. There is a classifying bundle EA + BA; let MA = EAx,M be the orbit space of the diagonal action of A on EAxM. The Bore1 equivariant cohomology ring of the A-space M is defined by the formula
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