A Decomposition Theorem for Cayley Graphs of Picard Group Quotients

@inproceedings{Rosenhouse2004ADT,
title={A Decomposition Theorem for Cayley Graphs of Picard Group Quotients},
author={Jason Rosenhouse},
year={2004}
}

The Picard group is defined as Γ = SL(2,Z[i]); the ring of 2× 2 matrices with Gaussian integer entries and determinant one. We consider certain graphs associated to quotients Γ/Γ(p) where p is a prime congruent to three mod four and Γ(p) is the congruence subgroup of level p. We prove a decomposition theorem on the vertices of these graphs, and use this decomposition to derive upper and lower bounds on their isoperimetric numbers.