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Invariant Functions with Respect to the Whitehead-Link

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Part of the Progress in Mathematics book series (PM, volume 260)

Abstract

We survey our construction of invariant functions on the real 3-dimensional hyperbolic space ℍ3 for the Whitehead-link-complement group WGL 2(ℤ[i]) and for a few groups commensurable with W. We make use of theta functions on the bounded symmetric domain \( \mathbb{D} \) of type I 2,2 and an embedding i : ℍ3\( \mathbb{D} \). The quotient spaces of ℍ3 by these groups are realized by these invariant functions. We review classical results on the λ-function, the j-function and theta constants on the upper half space; our construction is based on them.

Keywords

Whitehead link hyperbolic structure automorphic forms theta functions 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

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