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Betti numbers and injectivity radii
Author(s):
Marc
Culler;
Peter
B.
Shalen
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3919-3922.
MSC (2000):
Primary 57M50;
Secondary 57N10
Posted:
June 18, 2009
MathSciNet review:
2529901
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Abstract:
We give lower bounds on the maximal injectivity radius for a closed hyperbolic 3-manifold with first Betti number 2 under some additional topological hypotheses.
References:
- [1]
- Ian Agol, Marc Culler, and Peter B. Shalen, Singular surfaces, mod
 homology, and hyperbolic volume. I, arXiv:math.GT/0506396. To appear in Trans. Amer. Math. Soc.. - [2]
- Ian Agol, Peter A. Storm, and William P. Thurston, Lower bounds on volumes of hyperbolic Haken
 -manifolds, J. Amer. Math. Soc. 20 (2007), no. 4, 1053-1077 (electronic). With an appendix by Nathan Dunfield. MR 2328715 (2008i:53086) - [3]
- James W. Anderson, Richard D. Canary, Marc Culler, and Peter B. Shalen, Free Kleinian groups and volumes of hyperbolic
 -manifolds, J. Differential Geom. 43 (1996), no. 4, 738-782. MR 1412683 (98c:57012) - [4]
- Marc Culler and Peter B. Shalen, Paradoxical decompositions,
 -generator Kleinian groups, and volumes of hyperbolic  -manifolds, J. Amer. Math. Soc. 5 (1992), no. 2, 231-288. MR 1135928 (93a:57017) - [5]
- Marc Culler and Peter B. Shalen, Volumes of hyperbolic Haken manifolds. I, Invent. Math. 118 (1994), no. 2, 285-329. MR 1292114 (95g:57023)
- [6]
- Marc Culler and Peter B. Shalen, Volumes of hyperbolic Haken manifolds. II, Proc. Amer. Math. Soc. 125 (1997), no. 10, 3059-3067. MR 1422858 (97m:57022)
- [7]
- Andrew Przeworski, Cones embedded in hyperbolic manifolds, J. Differential Geom. 58 (2001), no. 2, 219-232. MR 1913942 (2003e:57030)
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Additional Information:
Marc
Culler
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045
Email:
culler@math.uic.edu
Peter
B.
Shalen
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045
Email:
shalen@math.uic.edu
DOI:
10.1090/S0002-9939-09-09966-3
PII:
S 0002-9939(09)09966-3
Received by editor(s):
February 12, 2009
Posted:
June 18, 2009
Additional Notes:
This work was partially supported by NSF grants DMS-0504975 and DMS-0608567
Dedicated:
Dedicated to José María Montesinos on the occasion of his 65th birthday
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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