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Collisions at infinity in hyperbolic manifolds

Published online by Cambridge University Press:  09 July 2013

D. B. MCREYNOLDS ,
ALAN W. REID  and
MATTHEW STOVER
D. B. MCREYNOLDS
Affiliation:
Purdue University e-mail: dmcreyno@math.purdue.edu
ALAN W. REID
Affiliation:
University of Texas at Austin e-mail: areid@math.utexas.edu
MATTHEW STOVER
Affiliation:
University of Michigan e-mail: stoverm@umich.edu
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Abstract

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of M. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont and Sisto.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 459 - 463
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

REFERENCES

[1]Bergeron, N.Premier nombre de Betti et spectre du laplacien de certaines variétés hyperboliques. Enseign. Math. 46 (2000), 109–137.Google Scholar
[2]Bergeron, N., Haglund, F. and Wise, D.Hyperplane sections in arithmetic hyperbolic manifolds. J. Lond. Math. Soc. (2) 83 (2011), 431–448.CrossRefGoogle Scholar
[3]Frigerio, R., Lafont, J.-F. and Sisto, A. Rigidity of high dimensional graph manifolds, arXiv:1107.2019.Google Scholar
[4]Haglund, F. and Wise, D.Special cube complexes, Geom. Funct. Anal. 17 (2008), 1551–1620.CrossRefGoogle Scholar
[5]Kolpakov, A. and Martelli, B. Hyperbolic four-manifolds with one cusp, arXiv:1303.6122.Google Scholar
[6]Long, D. D. and Reid, A. W.Surface Subgroups and Subgroup Separability in 3-Manifold Topology. (Publicacoes Matemáticas do IMPA, 2005).Google Scholar
[7]Long, D. D. and Reid, A. W.Subgroup separability and virtual retractions of groups. Topology 47 (2008), 137–159.CrossRefGoogle Scholar
[8]Lubotzky, A. and Segal, D.Subgroup Growth. Prog. Math. 212. (Birkhäuser, 2003).Google Scholar
[9]Maclachlan, C. and Reid, A. W.The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics 219 (Springer-Verlag, 2003).Google Scholar
[10]Raghunathan, M. S.Discrete subgroups of Lie Groups. Ergeb. Math. Grenzgeb. 68, Springer-Verlag, 1972.Google Scholar
[11]Ratcliffe, J. G.Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics 149 (Springer, 2006).Google Scholar
[12]Scott, G. P.Subgroups of surface groups are almost geometric. J. London Math. Soc. 17 (1978), 555–565. See also ibid Correction: J. London Math. Soc. 32 (1985), 217–220.CrossRefGoogle Scholar
[13]Stover, M.On the number of ends of rank one locally symmetric spaces. Geom. Topol. 17 (2013), no. 2, 905–924.CrossRefGoogle Scholar