On the Farrell and Jones warping deformation

نویسنده

  • Pedro Ontaneda
چکیده

The Farrell-Jones warping deformation is a powerful geometric construction that has been crucial in the proofs of many important contributions to the theory of manifolds of negative curvature. In this paper we study this construction in depth, in a more general setting, and obtain explicit quantitative results. The results in this paper are key ingredients in the problem of smoothing Charney-Davis strict hyperbolizations [6], [20]. Section 0. Introduction. Let g be a Riemannian metric on the n-sphere Sn. Consider the warped metric h = sinh2(t) g+ dt2 on Rn+1 − {0} = Sn × (0,∞). If g = σ Sn , the canonical round metric on Sn, then h is the (real) hyperbolic metric. But for general g the metric h is not hyperbolic. In [7] Farrell and Jones used the following method to deform the metric h to a hyperbolic metric in a ball of large radius 2α centered at the origin. For α > 0 consider the metric: hα(x, t) = sinh (t) (

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عنوان ژورنال:
  • J. London Math. Society

دوره 92  شماره 

صفحات  -

تاریخ انتشار 2015