no. 1
Sur la topologie de l’espace des opérateurs pseudodifférentiels inversibles d’ordre 0
Rochon, Frédéric1
1 State University of New York Department of Mathematics Stony Brook (USA)
Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 29-62.

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 sont aussi données.

The homotopy groups of the (stabilized) group G 0 (X) of invertible pseudodifferential operators of order zero acting on a smooth compact manifold X are given in terms of the K-theory of the cosphere bundle S * X. At the same time, it is shown that the subgroup of invertible compact perturbations of the identity is weakly retractible in G 0 (X). The results are also adapted to the case of suspended operators. This gives applications in index theory and for the residue determinant of Simon Scott.

DOI : 10.5802/aif.2343
Classification : 58B05, 58B15
Mots clés : opérateurs pseudodifférentiels, groupes d’homotopie, $K$-théorie, déterminant résiduel

Rochon, Frédéric 1

1 State University of New York Department of Mathematics Stony Brook (USA) 
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Rochon, Frédéric. Sur la topologie de l’espace des opérateurs pseudodifférentiels inversibles d’ordre 0. Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 29-62. doi : 10.5802/aif.2343. https://aif.centre-mersenne.org/articles/10.5802/aif.2343/

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