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CAT(0) 4-manifolds possessing a single tame point are Euclidean

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Abstract

The concepts of geometric and topological tame point are introduced for a space of nonpositive curvature. These concepts are applied to the characterization problem forCAT(0) 4-manifolds. It is shown that everyCAT(0)M 4 having a single (geometric or topological) tame point is homeomorphic toR 4. Davis and Januszkiewicz have recently constructedCAT(0)n-manifolds,M n withn ≥ 5 such that the set of tame points form a dense open subset ofM n, butM n ≠R n.

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  1. Department of Mathematics, Cornell University, 14853, Ithaca, NY

    Paul Thurston

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Thurston, P. CAT(0) 4-manifolds possessing a single tame point are Euclidean. J Geom Anal 6, 475–494 (1996). https://doi.org/10.1007/BF02921662

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