15 citations · 183 across the 38 of their papers we have counts for
13 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…
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…
Classifying closed 2-orbifolds with Euler characteristics
Whitney DuVal, John Schulte, Christopher Seaton +1
We determine the extent to which the collection of -Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orien…
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…
The index of a vector field on an orbifold with boundary
Elliot Paquette, Christopher Seaton
A Poincaré-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the…
Characteristic Classes of Bad Orbifold Vector Bundles
Christopher Seaton
We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit constructi…
A Complete Obstruction to the Existence of Nonvanishing Vector Fields on Almost-Complex, Closed, Cyclic Orbifolds
Christopher Seaton
We determine several necessary and sufficient conditions for a closed almost-complex orbifold with cyclic local groups to admit a nonvanishing vector field. These conditions ar…
Two Gauss-Bonnet and Poincaré-Hopf Theorems for Orbifolds with Boundary
Christopher Seaton
The goal of this work is to generalize the Gauss-Bonnet and Poincaré-Hopf Theorems to the case of orbifolds with boundary. We present two such generalizations, the first in the spi…