Abstract

We introduce the notion of a homotopy of product systems, and show that the
CuntzNicaPimsner algebras of homotopic product systems over N^k have
isomorphic Ktheory. As an application, we give a new proof that the Ktheory
of a 2graph C*algebra is independent of the factorisation rules, and we
further show that the Ktheory of any twisted kgraph C*algebra is independent
of the twisting 2cocycle. We also explore applications to Ktheory for the
C*algebras of singlevertex kgraphs, reducing the question of whether the
$K$theory is independent of the factorisation rules to a question about
pathconnectedness of the space of solutions to an equation of YangBaxter
type.