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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Pedro Ontaneda
Journal: Trans. Amer. Math. Soc. 355 (2003), 935-965
MSC (2000): Primary 53C20, 57Q25, 57R55
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 $PL$ 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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Additional Information

Pedro Ontaneda
Affiliation: Departamento de Matematica, Universidade Federal de Pernambuco, Cidade Universitaria, Recife, PE 50670-901, Brazil
Email: ontaneda@dmat.ufpe.br

DOI: https://doi.org/10.1090/S0002-9947-02-03076-3
Received by editor(s): April 12, 2001
Received by editor(s) in revised form: April 12, 2002
Published electronically: October 29, 2002
Additional Notes: This research was supported in part by CNPq, Brazil
Article copyright: © Copyright 2002 American Mathematical Society