The double of a hyperbolic manifold and non-positively curved exotic 𝑃𝐿 structures

Ontaneda, Pedro

doi:10.1090/S0002-9947-02-03076-3

The double of a hyperbolic manifold and non-positively curved exotic structures

Author: Pedro Ontaneda
Journal: Trans. Amer. Math. Soc. 355 (2003), 935-965
MSC (2000): Primary 53C20, 57Q25, 57R55
DOI: https://doi.org/10.1090/S0002-9947-02-03076-3
Published electronically: October 29, 2002
MathSciNet review: 1938740
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Abstract: We give examples of non-compact finite volume real hyperbolic manifolds of dimension greater than five, such that their doubles admit at least three non-equivalent smoothable structures, two of which admit a Riemannian metric of non-positive curvature while the third does not. We also prove that the doubles of non-compact finite volume real hyperbolic manifolds of dimension greater than four are differentiably rigid.

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