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

Zschumme, Pascal

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}$×⋯×$\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;$\mathbb{Z}$).

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Verlagsausgabe §
DOI: 10.5445/IR/1000129584
Veröffentlicht am 10.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0046-5755, 1572-9168
KITopen-ID: 1000129584
Erschienen in Geometriae dedicata
Verlag Springer
Vorab online veröffentlicht am 07.12.2020
Schlagwörter Homology; Geometric cycles; Locally symmetric spaces; Arithmetic groups; Quaternion algebras; Hyperbolic plane
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