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

Zschumme, Pascal

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}$×⋯×$\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
Nachgewiesen in Scopus
Web of Science
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