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The Journal of Geometric Analysis

, Volume 6, Issue 3, pp 475–494 | Cite as

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

  • Paul Thurston
Article
  • 41 Downloads

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 .

Math Subject Classification

51H20 51K10 57N13 57N10 

Key Words and Phrases

Curvature bounded from above convex metric tame point cell-like map homology manifold 1-LCC embedding 

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Copyright information

© Mathematica Josephina, Inc. 1996

Authors and Affiliations

  • Paul Thurston
    • 1
  1. 1.Department of MathematicsCornell UniversityIthaca

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