[{"type":"article-journal","title":"Geometric construction of homology classes in Riemannian manifolds covered by products of hyperbolic planes","issued":{"date-parts":[["2020"]]},"container-title":"Geometriae dedicata","DOI":"10.1007\/s10711-020-00574-y","author":[{"family":"Zschumme","given":"Pascal"}],"publisher":"Springer","ISSN":"0046-5755, 1572-9168","abstract":"We study the homology of Riemannian manifolds of finite volume that are covered by an r-fold product ($\\mathbb{H}$$^{2}$)$^{r}$=$\\mathbb{H}$$^{2}$\u00d7\u22ef\u00d7$\\mathbb{H}$$^{2}$ of hyperbolic planes. Using a variation of a method developed by Avramidi and Nguyen-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 homology group H$_{r}$(M;$\\mathbb{Z}$).","keyword":"Homology; Geometric cycles; Locally symmetric spaces; Arithmetic groups; Quaternion algebras; Hyperbolic plane","kit-publication-id":"1000129584"}]