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December, 2004 Special Cycles and Automorphic Forms on Arithmetically Defined Hyperbolic 3-Manifolds
Joachim Schwermer
Asian J. Math. 8(4): 837-860 (December, 2004).

Abstract

An orientable hyperbolic 3-manifold is isometric to the quotient of hyperbolic 3-space H3 by a discrete torsion free subgroup G of the group Iso(H3)0 of orientation -- preserving isometries of H3. The latter group is isomorphic to the (connected) group PGL2(C), the real Lie group SL2(C) modulo its center $\pm 1$. Generally, a discrete subgroup of PGL2(C) is called a Kleinian group. The group G is said to have finite covolume if H3/G has finite volume, and is said to be cocompact if H3/G is compact. Among hyperbolic 3-manifolds, the ones originating with arithmetically defined Kleinian groups form a class of special interest. Such an arithmetically defined 3-manifold H3/G is essentially determined (up to commensurability) by an algebraic number field k with exactly one complex place, an arbitrary (but possibly empty) set of real places and a quaternion algebra Dover k which ramifies (at least) at all real places of k. These arithmetic Kleinian groups fall naturally into two classes ...

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Joachim Schwermer. "Special Cycles and Automorphic Forms on Arithmetically Defined Hyperbolic 3-Manifolds." Asian J. Math. 8 (4) 837 - 860, December, 2004.

Information

Published: December, 2004
First available in Project Euclid: 13 June 2005

zbMATH: 1072.11029
MathSciNet: MR2127951

Rights: Copyright © 2004 International Press of Boston

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Vol.8 • No. 4 • December, 2004
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