6 papers
Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups
David Muñoz, Jorge Plazas, Mario Velásquez
In this article we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of He…
Noncommutative geometry of groups like
Jorge Plazas
We show that the Connes-Marcolli -system can be represented on the Big Picture, a combinatorial gadget introduced by Conway in order to understand various results about con…
Heisenberg modules over real multiplication noncommutative tori and related algebraic structures
Jorge Plazas
We review some aspects of the theory of noncommutative two-tori with real multiplication focusing on the role played by Heisenberg groups in the definition of algebraic structures…
Examples of noncommutative manifolds: complex tori and spherical manifolds
Jorge Plazas
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly int…
Quantum statistical mechanics and class field Theory
Jorge Plazas
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where s…
Arithmetic structures on noncommutative tori with real multiplication
Jorge Plazas
We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A. Polishchuk. Our aim is to understand how these rings give rise to an arithmeti…