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On the growth of $L^2$-invariants for sequences of lattices in Lie groups

Abstract:

We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge--Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini--Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze th...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4007/annals.2017.185.3.1

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Institution:
University of Oxford
Oxford college:
University College
Role:
Author
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MTA Renyi “Lendulet” Groups and Graphs Research Group More from this funder
Institut Universitaire de France More from this funder
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Grant:
Consolidator Grant 648017
Engineering and Physical Sciences Research Council More from this funder
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Publisher:
Department of Mathematics, Princeton University Publisher's website
Journal:
Annals of Mathematics Journal website
Volume:
185
Issue:
3
Pages:
711-790
Publication date:
2017-04-12
Acceptance date:
2016-12-18
DOI:
EISSN:
1939-8980
ISSN:
0003-486X
Source identifiers:
354423
Keywords:
Pubs id:
pubs:354423
UUID:
uuid:79ce917f-5c41-40b1-beea-824588db0268
Local pid:
pubs:354423
Deposit date:
2017-01-06

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