2010/09/10 by Goulnara Arzhantseva, Arzhantseva, Goulnara, Erik Guentner +1
Mathematics · #20F34 (Secondary) #20F65 (Primary) 20F69 #58G25 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Metric Geometry (math.MG) #math.FA #math.GR #math.MG #msc:20F34 #msc:20F65 #msc:20F69 #msc:58G25
paper · pdf · doi:10.48550/arxiv.1009.1966
7 pages
arxiv created 2010/09/10 · arxiv updated 2010/09/13
Given a closed Riemannian manifold M and a (virtual) epimorphism from the fundamental group of M onto a free group of rank 2, we construct a tower of finite sheeted regular covers Mnn=0∞ of M such that the first non-zero eigenvalues λ1(Mn) of the Laplacian converge to zero as n tends to infinity. This is the first 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 the fundamental group of M is supposed to surject onto an amenable group.