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

Cremaschi, Tommaso

doi:10.1090/ecgd/350

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

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:

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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Bibliographic Information

Tommaso Cremaschi
Affiliation: Department of Mathematics, University of Southern California, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467
MR Author ID: 1287432
Email: cremasch@usc.edu
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.
Journal: Conform. Geom. Dyn. 24 (2020), 118-130
DOI: https://doi.org/10.1090/ecgd/350
MathSciNet review: 4127908