This paper introduces a new interconnection network topology called the star-crossed cube (SCQ). The SCQ is observed to be superior to other contemporary networks in terms of various topological parameters such as diameter, cost, average distance, and message traffic density. The various performance metrics of the proposed network, including cost effectiveness and time-cost effectiveness, are f...

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C∗algebras o...

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C∗algebras o...

We consider the mixed gravitational-Yang-Mills anomaly as the coupling between the K-theory and K-homology of a C∗-algebra crossed product. The index theorem of Connes-Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras. MSC91: 19D55, 8...

We show that unital simple C-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C-algebras can be classified by their ordered K-theory. We apply this classification result to show that certain simple crossed products are isomorphic if they have the same ordered K-theory. In particular, irrational higher dimensional noncommutative tori of the form C(T)×θ...

It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.