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arXiv · 2407.06065

On The Evans Chain Complex

S. Joseph Lippert
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Abstract

We elaborate on the construction of the Evans chain complex for higher-rank graph $C^*$-algebras. Specifically, we introduce a block matrix presentation of the differential maps. These block matrices are then used to identify a wide family of higher-rank graph $C^*$-algebras with trivial K-theory. Additionally, in the specialized case where the higher-rank graph consists of one vertex, we are able to use the K\"unneth theorem to explicitly compute the homology groups of the Evans chain complex.

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S. Joseph Lippert. 2024-07-08. On The Evans Chain Complex. https://doi.org/10.1017/s0004972724000728

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