Mathematische Zeitschrift

, Volume 286, Issue 1–2, pp 291–323 | Cite as

Oeljeklaus–Toma manifolds and arithmetic invariants

Article

Abstract

We consider Oeljeklaus–Toma manifolds coming from number fields with precisely one complex place. Our general theme is to relate the geometry to the arithmetic. We show that just knowing the fundamental group allows us to recover the number field. We also show that this fails if there are more complex places. The first homology turns out to be related to an interesting ideal. We compute the volume in terms of the discriminant and regulator of the number field. Is there a conceptual reason for this? We explore this and see what happens if we (entirely experimentally) regard them as “baby siblings” of hyperbolic manifolds coming from number fields.

Mathematics Subject Classification

53C55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Albert Ludwig University of FreiburgFreiburgGermany

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