An explicit spine for the Picard modular group over the Gaussian integers

Let Γ\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D0 is a Γ-equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Γ. We explicitly construct a spine for the case of Γ=SU(2,1;Z[i]). The spine is then used to compute the cohomology of Γ\D with various local coefficients.