8 papers
Voltage quantum graphs and a Gross-Tucker theorem for quantum graphs
Björn Schäfer, Mariusz Tobolski
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group . A classical construction of Gross and Tucker associates to every voltage graph…
From length-preserving pushouts of graphs to one-surjective pullbacks of graph algebras
Piotr M. Hajac, Mariusz Tobolski
The unions of directed graphs are the simplest examples of pushouts of directed graphs. The conditions under which they contravariantly induce surjective gauge-equivariant pullback…
On morphisms of topological quivers
Mariusz Tobolski
We introduce regular morphisms of topological quivers and show that they give rise to a subcategory of the category of topological quivers and quiver morphisms. Our regularity cond…
Gluing topological graph C*-algebras
Atul Gothe, John Quigg, Mariusz Tobolski
We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topolo…
Principal Actions on Topological Quivers and Associated Operator Dynamics
Matthew Gillespie, Lucas Hall, Benjamin Jones +1
We study topological quivers admitting a free and proper action by a locally compact group together with their associated -algebras. On the topological side, we provid…
The covariant functoriality of graph algebras
Piotr M. Hajac, Mariusz Tobolski
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain…