Noncommutative geometry of groups like Γ₀(N)

الأصل · EN

We show that the Connes-Marcolli GL₂-system can be represented on the Big Picture, a combinatorial gadget introduced by Conway in order to understand various results about congruence subgroups pictorially. In this representation the time evolution of the system is implemented by Conway's distance between projective classes of commensurable lattices. We exploit these results in order to associate quantum statistical mechanical systems to congruence subgroups in a way appropriate for the study of monstrous moonshine.