Flat cycles in the homology of (m,R)/SO(m)
Abstract
In this paper we show that flat (m-1)-dimensional tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL(m,Z) (m,R)/SO(m). We also show that the dimension of the subspace of Hm-1( (m,R)/SO(m);Q) spanned by flat (m-1)-tori grows as one goes up in congruence covers.
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