Commensurability of hyperbolic manifolds with geodesic boundary
Geometriae Dedicata, ISSN: 0046-5755, Vol: 118, Issue: 1, Page: 105-131
2006
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Article Description
Suppose n ≥ 3, let M , M be n-dimensional connected complete finite-volume hyperbolic manifolds with nonempty geodesic boundary, and suppose that π (M ) is quasi-isometric to π (M ) (with respect to the word metric). Also suppose that if n=3, then ∂M and ∂M are compact. We show that M is commensurable with M . Moreover, we show that there exist homotopically equivalent hyperbolic 3-manifolds with non-compact geodesic boundary which are not commensurable with each other. We also prove that if M is as M above and G is a finitely generated group which is quasi-isometric to π (M), then there exists a hyperbolic manifold with geodesic boundary M′ with the following properties: M′ is commensurable with M, and G is a finite extension of a group which contains π (M′) as a finite-index subgroup. © Springer 2006.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=33744808038&origin=inward; http://dx.doi.org/10.1007/s10711-005-9028-x; http://link.springer.com/10.1007/s10711-005-9028-x; http://link.springer.com/content/pdf/10.1007/s10711-005-9028-x; http://link.springer.com/content/pdf/10.1007/s10711-005-9028-x.pdf; http://link.springer.com/article/10.1007/s10711-005-9028-x/fulltext.html; https://dx.doi.org/10.1007/s10711-005-9028-x; https://link.springer.com/article/10.1007/s10711-005-9028-x; http://www.springerlink.com/index/10.1007/s10711-005-9028-x; http://www.springerlink.com/index/pdf/10.1007/s10711-005-9028-x
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