Flat cycles in the homology of Γ\SL(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) \SL(m,R)/SO(m). We also show that the dimension of the subspace of H_{m-1}(Γ\SL(m,R)/SO(m);Q) spanned by flat (m-1)-tori grows as one goes up in congruence covers.

arXiv comment18 pages, 5 figures, added an explanation on page 12, updated bibliography

References in corpus (1)

• Periodic maximal flats are not peripheral

Cited by in corpus (1)

• Geometric construction of homology classes in Riemannian manifolds covered by products of hyperbolic planes