Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T03:06:41.640Z Has data issue: false hasContentIssue false

Collisions at infinity in hyperbolic manifolds

Published online by Cambridge University Press:  09 July 2013

D. B. MCREYNOLDS
Affiliation:
Purdue University e-mail: [email protected]
ALAN W. REID
Affiliation:
University of Texas at Austin e-mail: [email protected]
MATTHEW STOVER
Affiliation:
University of Michigan e-mail: [email protected]

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
Copyright
Copyright © Cambridge Philosophical Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bergeron, N.Premier nombre de Betti et spectre du laplacien de certaines variétés hyperboliques. Enseign. Math. 46 (2000), 109137.Google Scholar
[2]Bergeron, N., Haglund, F. and Wise, D.Hyperplane sections in arithmetic hyperbolic manifolds. J. Lond. Math. Soc. (2) 83 (2011), 431448.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), 15511620.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), 137159.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), 555565. 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, 905924.CrossRefGoogle Scholar