The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum
principal bundles over non affine bases. We study noncommutative principal bundles …

In this paper, we consider non-standard dynamics on the C∗-algebra associated with a
higher-rank graph Λ. These dynamics were first introduced by McNamara in his thesis, and …

Our main theorem is that the pullback of an associated noncommutative vector bundle
induced by an equivariant map of quantum principal bundles is a noncommutative vector …

The $ K_0 $-group of the C*-algebra of multipullback quantum complex projective plane is
known to be $\mathbb {Z}^ 3$, with one generator given by the C*-algebra itself, one given …

The multipullback quantization of complex projective spaces lacks the naive quantum CW-
complex structure because the quantization of an embedding of the $ n $-skeleton into the …

The representations of a $ k $-graph $ C^* $-algebra $ C^*(\Lambda) $ which arise from
$\Lambda $-semibranching function systems are closely linked to the dynamics of the $ k …

We give a complete classification of isomorphism classes of finitely generated projective
modules, or equivalently, unitary equivalence classes of projections, over the C*-algebra C …

We prove that the graph C*-algebra $ C^*(E) $ of a trimmable graph $ E $ is $ U (1) $-
equivariantly isomorphic to a pullback C*-algebra of a subgraph C*-algebra $ C^*(E'') $ and …

To unravel the structure of fundamental examples studied in noncommutative topology, we
prove that the graph C-algebra C. E/of a trimmable graph E is U. 1/-equivariantly isomorphic …

We elaborate on the construction of the Evans chain complex for higher-rank graph-
algebras with trivial K-theory. Additionally, in the specialised case where the higher-rank …