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A locally hyperbolic 3-manifold that is not hyperbolic


Author: Tommaso Cremaschi
Journal: Proc. Amer. Math. Soc. 146 (2018), 5475-5483
MSC (2010): Primary 57M50
DOI: https://doi.org/10.1090/proc/14176
Published electronically: September 4, 2018
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Abstract: We construct a locally hyperbolic 3-manifold $ M_\infty $ such that
$ \pi _1(M_\infty )$ has no divisible subgroup. We then show that $ M_\infty $ is not homeomorphic to any complete hyperbolic manifold. This answers a question of Agol.


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Additional Information

Tommaso Cremaschi
Affiliation: Department of Mathematics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467
Email: cremasch@bc.edu

DOI: https://doi.org/10.1090/proc/14176
Received by editor(s): December 16, 2017
Received by editor(s) in revised form: March 25, 2018
Published electronically: September 4, 2018
Additional Notes: The author gratefully acknowledges support from the U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network) and also from the grant DMS-1564410: Geometric Structures on Higher Teichmüller Spaces.
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society

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