We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spe...

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The Calgebra generated by the partial isometries is thus a quotient of the universal C-algebra for partial representations of the group, from which it inherits a crossed product structure, of an abelian C-algebra by a partial actio...

The aim of this paper is to clarify the relationship between Gromovhyperbolicity and amenability for planar maps.