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On Elliptic Curves in SL2(ℂ)/Γ.., Schanuel’s Conjecture and Geodesic Lengths

Published online by Cambridge University Press:  22 January 2016

Jörg Winkelmann
Jörg Winkelmann*
Affiliation:
Institut Elie Cartan (Mathématiques), Université Henri PoincaréNancy 1, B.P. 239, F-54506 Vandœuvre-les-Nancy, Cedex, France. [email protected]
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Abstract

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Let Γ be a discrete cocompact subgroup of SL2(ℂ). We conjecture that the quotient manifold X = SL2(ℂ) / Γ contains infinitely many non-isogenous elliptic curves and prove this is indeed the case if Schanuel’s conjecture holds. We also prove it in the special case where Γ ∩ SL2(∝) is cocompact in SL2(ℝ).

Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.

Keywords

22E4032M1032J1753C22
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 176 , 2004 , pp. 159 - 180
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

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