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Coarse non-amenability and covers with small eigenvalues

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Publikationsdatum 2012
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Mathematische Annalen
Volume (Issue) 354(3)
Seite(n) 863 - 870
Titel der Proceedings Mathematische Annalen
DOI 10.1007/s00208-011-0759-8.


Given a closed Riemannian manifold M and a (virtual) epimorphism 1(M)  F2 of the fundamental group onto a free group of rank 2, we construct a tower of nite sheeted regular covers fMng1 n=0 of M such that 1(Mn) ! 0 as n ! 1. This is the rst example of such a tower which is not obtainable up to uniform quasi-isometry (or even up to uniform coarse equivalence) by the previously known methods where 1(M) is supposed to surject onto an amenable group.