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Transactions of the American Mathematical Society

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

   
 
 

 

Counting cusped hyperbolic 3-manifolds that bound geometrically


Authors: Alexander Kolpakov and Stefano Riolo
Journal: Trans. Amer. Math. Soc. 373 (2020), 229-247
MSC (2010): Primary 57R90, 57M50, 20F55, 37F20
DOI: https://doi.org/10.1090/tran/7883
Published electronically: August 1, 2019
MathSciNet review: 4042873
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Abstract: We show that the number of isometry classes of cusped hyperbolic $ 3$-manifolds that bound geometrically grows at least super-exponentially with their volume, both in the arithmetic and non-arithmetic settings.


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Additional Information

Alexander Kolpakov
Affiliation: Institut de mathématiques, Rue Emile-Argand 11, 2000 Neuchâtel, Switzerland
Email: kolpakov.alexander@gmail.com

Stefano Riolo
Affiliation: Institut de mathématiques, Rue Emile-Argand 11, 2000 Neuchâtel, Switzerland
Email: stefano.riolo@unine.ch

DOI: https://doi.org/10.1090/tran/7883
Keywords: $3$-manifold, $4$-manifold, hyperbolic geometry, cobordism, geometric boundary.
Received by editor(s): February 14, 2019
Received by editor(s) in revised form: April 21, 2019
Published electronically: August 1, 2019
Additional Notes: The authors were supported by the Swiss National Science Foundation, project no. PP00P2-170560
Article copyright: © Copyright 2019 by the authors