Stability of Lie groupoid C*-algebras

In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the $C^*$- algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the groupoid has no orbit of dimension zero. We also prove an analogous theorem for singular foliations for which the holonomy groupoid as defined by I. Androulidakis and G. Skandalis is not Lie in general

Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions

The adiabatic groupoid $\mathcal{G}_{ad}$ of a smooth groupoid $\mathcal{G}$ is a deformation relating $\mathcal{G}$ with its algebroid. In a previous work, we constructed a natural action of $\mathbb{R}$ on the C*-algebra of zero order pseudodifferential operators on $\mathcal{G}$ and identified the crossed product with a natural ideal $J(\mathcal{G})$ of $C^*(\mathcal{G}_{ad})$. In the present paper we show that $C^*(\mathcal{G}_{ad})$ itself is a pseudodifferential extension of this crossed product in a sense introduced by Saad Baaj. Let us point out that we prove our results in a slightly more general situation: the smooth groupoid $\mathcal{G}$ is assumed to act on a C*-algebra $A$. We construct in this generalized setting the extension of order $0$ pseudodifferential operators $\Psi(A,\mathcal{G})$ of the associated crossed product $A\rtimes \mathcal{G}$. We show that $\mathbb{R}$ acts naturally on $\Psi(A,\mathcal{G})$ and identify the crossed product of $A$ by the action of the adiabatic groupoid $\mathcal{G}_{ad}$ with an extension of the crossed product $\Psi(A,\mathcal{G})\rtimes \mathbb{R}$. Note that our construction of $\Psi(A,\mathcal{G})$ unifies the ones of Connes (case $A=\mathbb{C}$) and of Baaj ($\mathcal{G}$ is a Lie group).Comment: appears in Bulletin des sciences math\'ematiques (2015

K-duality for stratified pseudomanifolds

This paper is devoted to the study of Poincar\'e duality in K-theory for general stratified pseudomanifolds. We review the axiomatic definition of a smooth stratification \fS of a topological space $X$ and we define a groupoid T^{\fS}X, called the \fS-tangent space. This groupoid is made of different pieces encoding the tangent spaces of the strata, and these pieces are glued into the smooth noncommutative groupoid T^{\fS}X using the familiar procedure introduced by A. Connes for the tangent groupoid of a manifold. The main result is that C^{*}(T^{\fS}X) is Poincar\'e dual to $C(X)$, in other words, the \fS-tangent space plays the role in $K$-theory of a tangent space for $X$

An index theorem for manifolds with boundary

In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary.Comment: 6 pages. Preprint submitted to the Academie des Science

Effects of Supplemental Whole Cottonseed on Weaned Calf Production

This study compared the effect of supplemental whole cottonseed in a weaned calf ration on cattle productivity. Feed is the main cost for livestock production. Whole cottonseed supplementation may increase production and reduce the cost of gain for the ration. During the study, 18 beef calves were weaned and split into two groups and fed, with and without WCS, for 50 days to determine the effect of supplemental whole cottonseed. Productivity was determined by measuring average daily gains for each group and comparing cost of gain for each ration. It was determined that WCS did increase productivity of weaned calves through showing a decrease in cost per pound of gain by $0.02 and increasing average daily gain by 0.36lbs

From Weak Woman to New Woman and Back: The Long Struggle to Legitimize Women Athletes in the U.S.

This paper details the complicated history of women in sport by looking at the changing popular image of women athletes from the late 19th century to today

A Teaching Professor Attending a Conference Called The Teaching Professor

The Teaching Professor was a conference held in New Orleans, LA in June 2023. I attended sessions and became more informed about how to better engage my students in the classroom by using group-oriented techniques that demonstrably increased participant conversation during the conference. Using rubrics to improve student performance and speed grading time was discussed at length. Useful resources were provided in all sessions

How Integrated Extension Programming Helps Market Cooperative Extension: The North Carolina Recommendation

In a contemporary society, Extension educational programming must consider the multiple community systems affected by identified issues. Recommendations based on a 2-year study process in North Carolina demonstrate how integrated educational programming is connected to marketing Extension. Two figures provide a visual of the concepts described