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Carla Farsi

Publications and source records attributed to Carla Farsi.

43 records · Page 3Linked to original sources
arXiv2013

Γ-extensions of the spectrum of an orbifold

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 union of the Laplace spectra of the Γ-sectors of the orbifold, and hence constitutes a Riemannian invariant that is directly related to the singular set of the orbifold. We compare the Γ-spectra of known examples of isospectral pairs and families of orbifolds and demonstrate that it many cases, isospectral orbifolds need not be Γ-isospectral. We additionally prove a version of Sunada's theorem that allows us to construct pairs of orbifolds that are Γ-isospectral for any choice of Γ.

math.DG↗
arXiv2009

Generalized orbifold Euler characteristics for general orbifolds and wreath products

We introduce the $Γ$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily global quotients the generalized orbifold Euler characteristics of Bryan-Fulman and Tamanoi. Each of these Euler characteristics is defined as the Euler-Satake characteristic of the space of $Γ$-sectors of the orbifold where $Γ$ is a finitely generated discrete group. We study the behavior of these characteristics under product operations applied to the group $Γ$ as well as the orbifold and establish their relationships to existing Euler characteristics for orbifolds. As applications, we generalize formulas of Tamanoi, Wang, and Zhou for the Euler characteristics and Hodge numbers of wreath symmetric products of global quotient orbifolds to the case of quotients by compact, connected Lie groups acting almost freely.

math.DG↗
arXiv2009

Generalized twisted sectors of orbifolds

For a finitely generated discrete group $Γ$, the $Γ$-sectors of an orbifold $Q$ are a disjoint union of orbifolds corresponding to homomorphisms from $Γ$ into a groupoid presenting $Q$. Here, we show that the inertia orbifold and $k$-multi-sectors are special cases of the $Γ$-sectors, and that the $Γ$-sectors are orbifold covers of Leida's fixed-point sectors. In the case of a global quotient, we show that the $Γ$-sectors correspond to orbifolds considered by other authors for global quotient orbifolds as well as their direct generalization to the case of an orbifold given by a quotient by a Lie group. Furthermore, we develop a model for the $Γ$-sectors corresponding to a generalized loop space.

math.DG↗
arXiv2008

Dirac Operators on Non-Compact Orbifolds

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 generalized orbifold Stokes'/Divergence theorem.

math.DG↗
arXiv2008

Nonvanishing vector fields on orbifolds

We introduce a complete obstruction to the existence of nonvanishing vector fields on a closed orbifold $Q$. Motivated by the inertia orbifold, the space of multi-sectors, and the generalized orbifold Euler characteristics, we construct for each finitely generated group $Γ$ an orbifold called the space of $Γ$-sectors of $Q$. The obstruction occurs as the Euler-Satake characteristics of the $Γ$-sectors for an appropriate choice of $Γ$; in the case that $Q$ is oriented, this obstruction is expressed as a cohomology class, the $Γ$-Euler-Satake class. We also acquire a complete obstruction in the case that $Q$ is compact with boundary and in the case that $Q$ is an open suborbifold of a closed orbifold.

math.DG↗
arXiv2007

An Orbifold Relative Index Theorem

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 theorem of Gromov and Lawson.

math.DG↗