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Sur la topologie de l’espace des opérateurs pseudodifférentiels inversibles d’ordre 0

Frédéric Rochon — 2008

Annales de l’institut Fourier

Les groupes d’homotopie du groupe (stabilisé) $G^{0} (X)$ des opérateurs pseudodifférentiels inversibles d’ordre zéro agissant sur une variété compacte sans bord $X$ sont calculés en termes de la $K$ -théorie du fibré cosphérique $S^{*} X$ . Du même coup, on montre que le sous-groupe des perturbations compactes inversibles de l’identité est faiblement rétractile dans $G^{0} (X)$ . Les résultats sont aussi adaptés au cas des opérateurs suspendus. Des applications à la théorie de l’indice et pour le déterminant résiduel de Simon Scott...

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