Growth of mod-2 homology in higher rank locally symmetric spaces

2018/01/28 by Fraczyk, Mikolaj · 1 citation
#57T15 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09283

Abstract

Let X be a higher rank symmetric space or a Bruhat-Tits building of dimension at least 2 such that the isometry group of X has property (T). We prove that for every torsion free lattice Γ⊂ \rm Isom X any homology class in H₁(Γ\backslash X,\mathbb F₂) has a representative cycle of total length o_X(\rm Vol(Γ\backslash X)). As an application we show that dim_{\mathbb F2} H₁(Γ\backslash X,\mathbb F₂)=o_X(\rm Vol(Γ\backslash X)).

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