Strong Jordan Separation and Applications to Rigidity
نویسنده
چکیده
We prove that simple, thick hyperbolic P-manifolds of dimension at least three exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension at least three. The key tool in the proof of these rigidity results is a strong form of the Jordan separation theorem, for maps from Sn → Sn+1 which are not necessarily injective.
منابع مشابه
2 00 4 Strong Jordan separation and applications to rigidity
In this paper, we extend the results of [10] to higher dimension. We prove that simple, thick hyperbolic P-manifolds of dimension ≥ 3 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension ≥ 3. The key tool in the proof of these rigidity results is a strong form of the Jordan separation theorem, for...
متن کامل1 3 Ju n 20 05 Strong Jordan separation and applications to rigidity .
In this paper, we extend the results of [14] to higher dimension. We prove that simple, thick hyperbolic P-manifolds of dimension ≥ 3 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension ≥ 3. The key tool in the proof of these rigidity results is a strong form of the Jordan separation theorem, for...
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