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


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 ...


Download Citation

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


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

zbMATH: 1072.11029
MathSciNet: MR2127951

Rights: Copyright © 2004 International Press of Boston


Vol.8 • No. 4 • December, 2004
Back to Top