Counting flat cycles in the homology of locally symmetric manifolds
with D. Studenmund
arxiv: 2206.11986
Locally symmetric spaces like SL(n,ℤ)\SL_n(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.
Note: there is a simpler proof of the main results, which we learned from a referee. This has not yet been incorporated into the draft.