14 citations · 47 across the 28 of their papers we have counts for
36 papers
Orbit-breaking in Deaconu-Renault groupoids and models for UCT Kirchberg algebras
Robin J. Deeley, Ian F. Putnam, Karen R. Strung
We generalize the concept of orbit-breaking from the case of a homeomorphism to the case of a surjective local homeomorphism. This method creates open subgroupoids of the Deaconu--…
Bordisms and unbounded -theory
Robin J. Deeley, Magnus Goffeng, Bram Mesland
This monograph studies -theory in its unbounded model. The central object is the -bordism group obtained by imposing the -bordism relation on unbounded -cycles. In…
A trace pairing and Elliott invariant for groupoid homology
Robin Deeley, Rufus Willett
For an étale groupoid, we define a pairing between the Crainic-Moerdijk groupoid homology and the simplex of invariant Borel probability measures on the base space. The main novelt…
Synchronizing Dynamical Systems: Finitely presented systems and Ruelle algebras
Robin J. Deeley, Andrew M. Stocker
The main goals of the present paper are to determine the structure of the -algebras associated to a finitely presented system and to develop the basic theory of the Ruelle…
The rational HK-conjecture: transformation groupoids and a revised version
Robin J. Deeley, Rufus Willett
We prove the rational HK-conjecture for a large class of transformation groupoids in the case when the relevant action has torsion-free stabilizers. A revised version of the ration…
Wieler solenoids: non-Hausdorff expansiveness, Cuntz-Pimsner models, and functorial properties
Robin J. Deeley, Menevse Eryüzlü, Magnus Goffeng +1
Building on work of Williams, Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this resu…
Invariants for the Smale space associated to an expanding endomorphism of a flat manifold
Rachel Chaiser, Maeve Coates-Welsh, Robin J. Deeley +7
We study invariants associated to Smale spaces obtained from an expanding endomorphism on a (closed connected Riemannian) flat manifold. Specifically, the relevant invariants are t…
Synchronizing Dynamical Systems: Shift Spaces and -Theory
Robin J Deeley, Andrew M Stocker
Building on our previous work, we give a thorough presentation of the techniques developed for synchronizing dynamical systems in the special case of synchronizing shift spaces. Fo…
Synchronizing Dynamical Systems: their groupoids and -algebras
Robin J. Deeley, Andrew M. Stocker
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic -algebras for an expansive dynamical system. In this paper we…
Fell algebras, groupoids, and projections
Robin J. Deeley, Magnus Goffeng, Allan Yashinski
Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous trace -algebras. At…
A counterexample to the HK-conjecture that is principal
Robin J. Deeley
Scarparo has constructed counterexamples to Matui's HK-conjecture. These counterexample and other known counterexamples are essentially principal but not principal. In the present…
Minimal homeomorphisms and topological -theory
Robin J. Deeley, Ian F. Putnam, Karen R. Strung
The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these…
Constructions in minimal amenable dynamics and applications to the classification of -algebras
Robin J. Deeley, Ian F. Putnam, Karen R. Strung
We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that…
Non-homogeneous extensions of Cantor minimal systems
Robin J. Deeley, Ian F. Putnam, Karen R. Strung
Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde an…
Smale space C*-algebras have nonzero projections
Robin J. Deeley, Magnus Goffeng, Allan Yashinski
The main result of the present paper is that the stable and unstable C*-algebras associated to a mixing Smale space always contain nonzero projections. This gives a positive answer…
The stable algebra of a Wieler solenoid: inductive limits and K-theory
Robin J. Deeley, Allan Yashinski
Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her cons…
Group actions on Smale space C*-algebras
Robin J. Deeley, Karen R. Strung
Group actions on a Smale space and the actions induced on the C*-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on…
Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property
Robin J. Deeley, Magnus Goffeng
We study Chern characters and the assembly mapping for free actions using the framework of geometric -homology. The focus is on the relative groups associated with a group homom…
A signed version of Putnam's homology theory: Lefschetz and zeta functions
Robin J. Deeley
A signed version of Putnam homology for Smale spaces is introduced. Its definition, basic properties and associated Lefschetz theorem are outlined. In particular, zeta functions as…
Wieler solenoids, Cuntz-Pimsner algebras and K-theory
Robin J. Deeley, Magnus Goffeng, Bram Mesland +1
We study irreducible Smale spaces with totally disconnected stable sets and their associated -theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict…
Nuclear dimension and classification of C*-algebras associated to Smale spaces
Robin J. Deeley, Karen R. Strung
We show that the homoclinic C*-algebras of mixing Smale spaces are classifiable by the Elliott invariant. To obtain this result, we prove that the stable, unstable, and homoclinic…
Relative geometric assembly and mapping cones, Part I: The geometric model and applications
Robin J. Deeley, Magnus Goffeng
Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric -homology. The properties of the geometric assembly map are stu…
Dynamical correspondences for Smale spaces
Robin J. Deeley, D. Brady Killough, Michael F. Whittaker
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of fi…
The bordism group of unbounded KK-cycles
Robin J. Deeley, Magnus Goffeng, Bram Mesland
We consider Hilsum's notion of bordism as an equivalence relation on unbounded -cycles and study the equivalence classes. Upon fixing two -algebras, and a -subalgebra d…