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

Zschumme, Pascal

doi:10.1007/s10711-020-00574-y

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

Zschumme, Pascal ¹
¹ Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)

Abstract:

We study the homology of Riemannian manifolds of finite volume that are covered by an r-fold product (

H

^{2}

)

^{r}

H

^{2}

×⋯×

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;

Z

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
Band	213
Seiten	191–210
Vorab online veröffentlicht am	07.12.2020
Schlagwörter	Homology; Geometric cycles; Locally symmetric spaces; Arithmetic groups; Quaternion algebras; Hyperbolic plane
Nachgewiesen in	Dimensions Scopus Web of Science OpenAlex

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Verlagsausgabe

DOI: 10.5445/IR/1000129584

Veröffentlicht am 10.02.2021

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Originalveröffentlichung
DOI: 10.1007/s10711-020-00574-y

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

Abstract: