25 citations · 122 across the 32 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
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…
Γ-extensions of the spectrum of an orbifold
Carla Farsi, Emily Proctor, Christopher Seaton
We introduce the Γ-extension of the spectrum of the Laplacian of a Riemannian orbifold, where Γis a finitely generated discrete group. This extension, called the Γ-spectrum, is the…
Stratifications of inertia spaces of compact Lie group actions
Carla Farsi, Markus J. Pflaum, Christopher Seaton
We study the topology of the inertia space of a smooth -manifold where is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demo…
Generalized orbifold Euler characteristics for general orbifolds and wreath products
Carla Farsi, Christopher Seaton
We introduce the -Euler-Satake characteristics of a general orbifold presented by an orbifold groupoid , generalizing to orbifolds that are not necessarily glob…
Generalized twisted sectors of orbifolds
Carla Farsi, Christopher Seaton
For a finitely generated discrete group , the -sectors of an orbifold are a disjoint union of orbifolds corresponding to homomorphisms from into a groupoid presenting…
Nonvanishing vector fields on orbifolds
Carla Farsi, Christopher Seaton
We introduce a complete obstruction to the existence of nonvanishing vector fields on a closed orbifold . Motivated by the inertia orbifold, the space of multi-sectors, and the…
An Orbifold Relative Index Theorem
Carla Farsi
In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated the…
Dirac Operators on Non-Compact Orbifolds
Carla Farsi
In this paper we prove that Dirac operators on non-compact complete orbifolds which are sufficiently regular at infinity, admit a unique extension. Additonally, we prove a generali…