Counting flat cycles in the homology of locally symmetric spaces

Bena Tshishiku; Daniel Studenmund

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Counting flat cycles in the homology of locally symmetric spaces

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arxiv 2206.11986 v1 pith:4HZA3EJJ submitted 2022-06-23 math.NT math.GRmath.GT

Counting flat cycles in the homology of locally symmetric spaces

Daniel Studenmund , Bena Tshishiku This is my paper

classification math.NT math.GRmath.GT

keywords locallyspacessymmetriccyclesflathomologymathbbbackslash

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Locally symmetric spaces like $SL(n,\mathbb Z)\backslash SL_n(\mathbb R)/SO(n)$ contain immersed compact flat manifolds of dimension equal to the real rank. We give a lower bound for the contribution of these cycles to the homology of congruence covers. Similar results are proved for other families of locally symmetric spaces.

Counting flat cycles in the homology of locally symmetric spaces

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