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Let M be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary TV of positive scalar curvature. We show that under these conditions, jy n (M;Z) = 0 and in particular N must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.
Witten et al. (Fri,) studied this question.
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