We study the homology of Riemannian manifolds of finite volume that are covered by a product of r copies of the hyperbolic plane. Using a variation of a method developed by Avramidi and Nyguen-Phan, we show that any such manifold M possesses, up to finite coverings, an arbitrarily large number of compact oriented flat totally geodesic r-dimensional submanifolds whose fundamental classes are linearly independent in the r-th homology group of M.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/9809
[4] http://www.mpim-bonn.mpg.de/node/10046/program?page=last
[5] http://www.mpim-bonn.mpg.de/node/10046/abstracts