Abstract
Abstract
Using a result of Vdovina, we may associate to each complete connected bipartite graph
$\kappa $
a two-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
$C^{\star }$
-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.
Funder
Engineering and Physical Sciences Research Council
Publisher
Cambridge University Press (CUP)
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