25 citations · 122 across the 32 of their papers we have counts for
36 papers
The universal Euler characteristic and Burnside group for definable groupoids
Carla Farsi, Emily Proctor, Christopher Seaton
We introduce the universal Euler characteristic of orbit space definable groupoids, a class of groupoids containing cocompact proper Lie groupoids as well as translation groupoids…
Isometry groups of inductive limits of metric spectral triples and Gromov-Hausdorff convergence
Jacopo Bassi, Roberto Conti, Carla Farsi +1
In this paper we study the groups of isometries and the set of bi-Lipschitz automorphisms of spectral triples from a metric viewpoint, in the propinquity framework of Latremoliere.…
Convergence of inductive sequences of spectral triples for the spectral propinquity
Carla Farsi, Frederic Latremoliere, Judith Packer
In the context of metric geometry, we introduce a new necessary and sufficient condition for the convergence of an inductive sequence of quantum compact metric spaces for the Gromo…
Spectral Triples for Noncommutative Solenoids and a Wiener's lemma
Carla Farsi, Therese Basa Landry, Nadia S. Larsen +1
In this paper we construct odd finitely summable spectral triples based on length functions of bounded doubling on noncommutative solenoids. Our spectral triples induce a Leibniz L…
Bicategories of Action Groupoids
Carla Farsi, Laura Scull, Jordan Watts
We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences à la…
Irreducibility and monicity for representations of -graph -algebras
Carla Farsi, Elizabeth Gillaspy, Daniel Gonçalves
The representations of a -graph -algebra which arise from -semibranching function systems are closely linked to the dynamics of the -graph . In this paper…
The spectra of digraphs with Morita equivalent -algebras
Carla Farsi, Emily Proctor, Christopher Seaton
Eilers et al. have recently completed the geometric classification of unital graph -algebras up to Morita equivalence using a set of moves on the corresponding digraphs. We…
Cocycles on Certain Groupoids Associated to -Actions
Carla Farsi, Leonard Huang, Alex Kumjian +1
We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and -a…
Orbifold Euler characteristics of non-orbifold groupoids
Carla Farsi, Christopher Seaton
For a finitely presented discrete group , we introduce two generalizations of the orbifold Euler characteristic and -orbifold Euler characteristic to a class of proper topolo…
Classifying spaces and Bredon (co)homology for transitive groupoids
Carla Farsi, Laura Scull, Jordan Watts
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomol…
Ample groupoids: equivalence, homology, and Matui's HK conjecture
Carla Farsi, Alex Kumjian, David Pask +1
We investigate the homology of ample Hausdorff groupoids. We establish that a number of notions of equivalence of groupoids appearing in the literature coincide for ample Hausdorff…
Generalized gauge actions on -graph -algebras: KMS states and Hausdorff structure
Carla Farsi, Elizabeth Gillaspy, Nadia S. Larsen +1
For a finite, strongly connected -graph , an Huef, Laca, Raeburn and Sims studied the KMS states associated to the preferred dynamics of the -graph -algebra .…
Purely atomic representations of higher-rank graph C*-algebras
Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2
We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equi…
Spectral triples for higher-rank graph -algebras
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this note, we present a new way to associate a spectral triple to the noncommutative -algebra of a strongly connected finite higher-rank graph . We generalize a…
Monic representations of finite higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2
In this paper we define the notion of monic representation for the -algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic r…
Representations of higher-rank graph -algebras associated to -semibranching function systems
Carla Farsi, Elizabeth Gillaspy, Palle E. T. Jorgensen +2
In this paper, we discuss a method of constructing separable representations of the -algebras associated to strongly connected row-finite -graphs . We begin by giving an…
Spectral triples and wavelets for higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph , via the infinite path space of . Moreover, we prove t…
Separable representations of higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2
In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of -algebras associated to strongly connected…
Rank-two Milnor idempotents for the multipullback quantum complex projective plane
Carla Farsi, Piotr M. Hajac, Tomasz Maszczyk +1
The -group of the C*-algebra of multipullback quantum complex projective plane is known to be , with one generator given by the C*-algebra itself, one given by t…
Wavelets and spectral triples for higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this paper, we present two new ways to associate a spectral triple to a higher-rank graph . Moreover, we prove that these spectral triples are intimately connected to the wav…
Approximating orbifold spectra using collapsing connected sums
Carla Farsi, Emily Proctor, Christopher Seaton
For a closed Riemannian orbifold , we compare the spectra of the Laplacian, acting on functions or differential forms, to the Neumann spectra of the orbifold with boundary given…
Wavelets and spectral triples for fractal representations of Cuntz algebras
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this article we provide an identification between the wavelet decompositions of certain fractal representations of algebras of directed graphs of M. Marcolli and A. Paoluc…
Wavelets and graph -algebras
Carla Farsi, Elizabeth Gillaspy, Sooran Kang +1
Here we give an overview on the connection between wavelet theory and representation theory for graph -algebras, including the higher-rank graph -algebras of A. Kumj…
Differentiable stratified groupoids and a de Rham theorem for inertia spaces
Carla Farsi, Markus J. Pflaum, Christopher Seaton
We introduce the notions of a differentiable groupoid and a differentiable stratified groupoid, generalizations of Lie groupoids in which the spaces of objects and arrows have the…