Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The K-theory of the C*-algebras of 2-rank graphs associated to complete
  bipartite graphs   Using a result of Vdovina, we may associate to each complete connected
bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile
complex, whose link at each vertex is $\kappa$. We regard the tile complex in
two different ways, each having a different structure as a $2$-rank graph. To
each $2$-rank graph is associated a universal C*-algebra, for which we compute
the K-theory, thus providing a new infinite collection of $2$-rank graph
algebras with explicit K-groups. We determine the homology of the tile
complexes, and give generalisations of the procedures to complexes and systems
consisting of polygons with a higher number of sides.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
1
The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn