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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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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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