Invariant functions with respect to the Whitehead-Link

Abstract

We survey our construction of invariant functions on the real 3-dimensional hyperbolic space ℍ3 for the Whitehead-link-complement group W ⊂ GL 2(ℤ[i]) and for a few groups commensurable with W. We make use of theta functions on the bounded symmetric domain D of type I 2,2 and an embedding i : ℍ3 → 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.