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

David Pask·Adam Rennie·Aidan Sims
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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.

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David Pask, Adam Rennie, Aidan Sims. 2007-01-19. Noncommutative manifolds from graph and $k$-graph $C^*$-algebras. https://arxiv.org/abs/math/0701527

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