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Conformal Geometry and Dynamics

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A locally hyperbolic 3-manifold that is not homotopy equivalent to any hyperbolic 3-manifold


Author: Tommaso Cremaschi
Journal: Conform. Geom. Dyn. 24 (2020), 118-130
DOI: https://doi.org/10.1090/ecgd/350
Published electronically: June 17, 2020
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Abstract | References | Additional Information

Abstract: We construct a locally hyperbolic 3-manifold $ M$ such that $ \pi _1(M)$ has no divisible subgroups. We then show that $ M$ is not homotopy equivalent to any complete hyperbolic manifold.


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Additional Information

Tommaso Cremaschi
Affiliation: Department of Mathematics, University of Southern California, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467
Email: cremasch@usc.edu

DOI: https://doi.org/10.1090/ecgd/350
Received by editor(s): December 24, 2018
Received by editor(s) in revised form: November 12, 2019
Published electronically: June 17, 2020
Additional Notes: The author gratefully acknowledges support from the U.S. National Science Foundation grant DMS-1564410: Geometric Structures on Higher Teichmüller Spaces.
Article copyright: © Copyright 2020 American Mathematical Society