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Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques

- Alexandre Baldare
- Philosophy
- 16 February 2018

Le probleme de l'indice est de calculer l'indice d'un operateur elliptique en termes topologiques. Ce probleme fut resolu par M. Atiyah et I. Singer en 1963 dans "The index of elliptic operators on… Expand

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Fredholm conditions for operators invariant with respect to compact Lie group actions.

- Alexandre Baldare, R. Come, V. Nistor
- Mathematics
- 7 December 2020

Let $G$ be a compact Lie group acting smoothly on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $G$--invariant, classical pseudodifferential operator acting between sections of… Expand

The index of G-transversally elliptic families in KK-theory

- Alexandre Baldare
- Mathematics
- 29 March 2018

We define and study the index map for families of G-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of the… Expand

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The index of leafwise G-transversally elliptic operators on foliations

- Alexandre Baldare, Moulay-Tahar Benameur
- Mathematics
- 8 January 2020

We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group… Expand

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The index of G-transversally elliptic families II

- Alexandre Baldare
- Mathematics
- 13 September 2018

We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic and… Expand

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Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components

- Alexandre Baldare, R. Come, M. Lesch, V. Nistor
- Mathematics
- 2 April 2020

Let $\Gamma$ be a finite group acting on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical pseudodifferential operator acting between sections of two… Expand

Fredholm conditions for restrictions of invariant pseudodifferential operators to isotypical components

Let Γ be a finite group acting on a smooth, compact manifold M , let P ∈ ψ(M ;E0, E1) be a Γ-invariant, classical pseudodifferential operator acting between sections of two vector bundles Ei → M , i… Expand

Fredholm conditions for invariant operators: finite abelian groups and boundary value problems

- Alexandre Baldare, R. Come, M. Lesch, V. Nistor
- Mathematics
- 5 November 2019

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth,… Expand

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The index of G-transversally elliptic families in cohomology.

- Alexandre Baldare
- Mathematics
- 29 March 2018

We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic and… Expand

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