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arXiv · 2407.00298

Real and complex K-theory for higher rank graph algebras arising from cube complexes

Jeffrey L Boersema·Alina Vdovina
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Abstract

Using the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank graphs we consider arise from double-covers of cube complexes. By considering the real and complex $K$-theory together, we are able to carry these computations much further than might be possible considering complex $K$-theory alone. As these algebras are classified by $K$-theory, we are able to characterize the isomorphism classes of the graph algebras in terms of the combinatorial and number-theoretic properties of the construction ingredients.

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Jeffrey L Boersema, Alina Vdovina. 2024-12-12. Real and complex K-theory for higher rank graph algebras arising from cube complexes. https://doi.org/10.2140/akt.2025.10.55

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