The KK-groups and the index theory of certain comparison C∗C^*-algebras

We compute the $K$-theory of comparison $C^*$-algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our calculation is obtained by showing that the comparison algebras are a homomorphic image of a groupoid $C^*$-algebra. We then prove an index theorem with values in the $K$-theory groups of the comparison algebra.Comment: 15 page

Groupoids and pseudodifferential calculus on manifolds with corners

AbstractWe associate to any manifold with corners (even with non-embedded hyperfaces) a (non-Hausdorff) longitudinally smooth Lie groupoid, on which we define a pseudodifferential calculus. This calculus generalizes the b-calculus of Melrose, defined for manifolds with embedded corners. The groupoid of a manifold with corners is shown to be unique up to equivalence for manifolds with corners of same codimension. Using tools from the theory of C∗-algebras of groupoids, we also obtain new proofs for the study of b-calculus

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

Pour une société apprenante

Inscrite dans la loi pour l\u27enseignement supérieur et la recherche du 23 juillet 2013, la stratégie nationale de l\u27enseignement supérieur (StraNES) a pour ambition de définir les objectifs nationaux engageant l\u27avenir à l\u27horizon des 10 prochaines années et de proposer les moyens de les atteindre. Ce rapport est issu d\u27un large processus de concertation auprès des acteurs et parties prenantes de l\u27enseignement supérieur et des chercheurs et observateurs rencontrés, il fait suite à un rapport d\u27étape destiné à présenter une première vision de la stratégie nationale de l\u27enseignement supérieur remis le 9 juillet 2014. Le rapport identifie cinq axes stratégiques construire une société apprenante et soutenir notre économie, développer la dimension européenne et l\u27internationalisation de notre enseignement supérieur, favoriser une réelle accession sociale et agir pour l\u27inclusion, inventer l\u27éducation supérieure du XXIème siècle, répondre aux aspirations de la jeunesse ainsi que trois leviers dessiner un nouveau paysage pour l\u27enseignement supérieur, écouter et soutenir les femmes et les hommes qui y travaillent, investir pour la société apprenante

Boutet de Monvel's Calculus and Groupoids I

17 pagesInternational audienceCan Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra $\Psi^0(G)$ of pseudodifferential operators on some Lie groupoid $G$? If it could, the kernel ${\mathcal G}$ of the principal symbol homomorphism would be isomorphic to the groupoid \mbox{$C^*$-algebra} $C^*(G)$. While the answer to the above question remains open, we exhibit in this paper a groupoid $G$ such that $C^*(G)$ possesses an ideal ${\mathcal I}$ isomorphic to ${\mathcal G}$. %ES, the kernel of the principal symbol homomorphism on Boutet de Monvel's algebra. In fact, we prove first that ${\mathcal G}\simeq\Psi\otimes{\mathcal K}$ with the $C^*$-algebra $\Psi$ generated by the zero order pseudodifferential operators on the boundary and the algebra $\mathcal K$ of compact operators. As both $\Psi\otimes \mathcal K$ and $\mathcal I$ are extensions of $C(S^*Y)\otimes {\mathcal{K}}$ by ${\mathcal{K}}$ ($S^*Y$ is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic

Stakeholders’ views on effective employment support strategies for autistic university students and graduates entering the world of work

Purpose This paper aims to examine effective support strategies for facilitating the employment of autistic students and graduates by answering the following research question: What constitutes effective employment support for autistic students and graduates? Design/methodology/approach Data were collected using the method of empathy-based stories (MEBS) as part of a multinational European project's Web-based survey. The data consisted of 55 writings about effective strategies and 55 writings about strategies to ]avoid when working with autistic students and graduates. The material was analysed using qualitative inductive content analysis. Narratives were created to illustrate desirable and undesirable environments and processes as they would be experienced by students, supported by original excerpts from the stories. Findings The analysis revealed that effective employment support for autistic students and graduates comprised three dimensions of support activity: practices based on the form and environment of support, social interaction support and autism acceptance and awareness. These dimensions were present in both recommended and not recommended support strategy writings. Originality/value The results add to the literature on autism and employment with its focus on the novel context of autistic university students and graduates. Effective strategies will be based on person-centred planning, to include not only the individual impact of autism but also individual career goals, workplace characteristics in the chosen field, employer needs and allocation of the right support. There is no one-size-fits-all strategy, but rather an individualized process is needed, focused on the identification of strengths, the adaptation of employment and work processes and improved understanding and acceptance of autism by management, colleagues and administration in the workplace.Peer reviewe