Remarks on flat and differential $K$-theory

Ho, Man-Ho

Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 1, pp. 91-101.

Dans cette note, nous prouvous certains résultats en $K$-théories plate et différentielle. La premier est une preuve de la compatibilité de l’indice topologique différentiel et de l’indice topologique plat par un calcul direct. Le second est un isomorphisme explicite entre les $K$-théories différentielles de Bunke-Schick et de Freed-Lott.

In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$-theory and Freed-Lott differential $K$-theory.

Classification : 19L50, 58J20
Keywords: differential $K$-theory, topological index
Mot clés : différentielle $K$-théorie, indice topologique

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