Noncommutative manifolds from graph and $k$-graph $C^*$-algebras

Abstract

In previous papers, we constructed smooth (1,\infty)-summable semfinite spectral triples for graph algebras with a faithful trace, and (k,\infty)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes' conditions for noncommutative manifolds.

29 pages, 1 figure, uses picTeX