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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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.