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Rank and genus of 3-manifolds


Author: Tao Li
Journal: J. Amer. Math. Soc. 26 (2013), 777-829
MSC (2010): Primary 57M05, 57M27, 57M50, 57N10
DOI: https://doi.org/10.1090/S0894-0347-2013-00767-5
Published electronically: February 27, 2013
MathSciNet review: 3037787
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Abstract: We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.


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Additional Information

Tao Li
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Email: taoli@bc.edu

DOI: https://doi.org/10.1090/S0894-0347-2013-00767-5
Received by editor(s): September 6, 2011
Received by editor(s) in revised form: September 27, 2012
Published electronically: February 27, 2013
Additional Notes: The author was partially supported by NSF grants DMS-1005556 and DMS-0705285
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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