Abért, Miklós and Bergeron, Nicolas and Biringer, Ian and Gelander, Tsachik (2023) Convergence of normalized Betti numbers in nonpositive curvature. DUKE MATHEMATICAL JOURNAL. ISSN 00127094

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Abstract
We study the convergence of volumenormalized Betti numbers in BenjaminiSchramm convergent sequences of nonpositively curved manifolds with finite volume. In particular, we show that if X is an irreducible symmetric space of noncompact type, X 6 = H3, and (Mn) is any BenjaminiSchramm convergent sequence of finite volume Xmanifolds, then the normalized Betti numbers bk(Mn)/vol(Mn) converge for all k. As a corollary, if X has higher rank and (Mn) is any sequence of distinct, finite volume Xmanifolds, the normalized Betti numbers of Mn converge to the L2 Betti numbers of X. This extends our earlier work with Nikolov, Raimbault and Samet in [1], where we proved the same convergence result for uniformly thick sequences of compact Xmanifolds. One of the novelties of the current work is that it applies to all quotients M = Γ\X where Γ is arithmetic; in particular, it applies when Γ is isotropic.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  03 Apr 2023 08:18 
Last Modified:  03 Apr 2023 08:18 
URI:  http://real.mtak.hu/id/eprint/163252 
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