Related papers: Topological spaces associated to higher-rank graph…
We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either contains no cycle with an entrance, or is cofinal. We also…
In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud…
We consider families of reductive complexes related by level-raising operators and originating from an associative algebra. In the main theorem it is shown that the multiple cohomology of that complexes is given by the factor space of…
We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate $C^*$-correspondences. We use this to calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger algebras of…
We give two new conditions on topological $k$-graphs that are equivalent to the Yeend's aperiodicity Condition (A). Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new…
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
For Hamiltonian circle actions on compact, connected, four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as an algebra over the equivariant cohomology of a point. This…
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…
Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…
We define branching systems for finitely aligned higher-rank graphs. From these we construct concrete representations of higher-rank graph C*-algebras on Hilbert spaces. We prove a generalized Cuntz-Krieger uniqueness theorem for periodic…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…
We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…
A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set of M into k distinct orbits, we say that M is a k-orbit…
We construct Grassmann spaces associated with the incidence geometry of regular and tangential subspaces of a symplectic copolar space, show that the underlying metric projective space can be recovered in terms of the corresponding…
A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct…
We construct a cobordism group for embedded graphs in two different ways, first by using sequences of two basic operations, called "fusion" and "fission", which in terms of cobordisms correspond to the basic cobordisms obtained by attaching…
This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…
Given an algebraic structure on the homology of a chain complex, we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this structure at the homology level. Our algebraic structures are…