Index theorey and Non-Commutative Geometry. II. Dirac operators and index bundles

Moulay Tahar Benameur (1) , James Heitsch (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Mathematics, Statistics, and Computer Science

When the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the $K-$theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

Mots clés: foliations; index; cyclic homology; chern-connes character

Domaines: Topologie géométrique [math.GT]; Algèbres d'opérateurs [math.OA]; K-théorie et homologie [math.KT]

Moulay Tahar Benameur, James Heitsch. Index theorey and Non-Commutative Geometry. II. Dirac operators and index bundles. Journal of K-theory , 2008, 1 (2), pp.305-356. ⟨10.1017/is007011012jkt007⟩. ⟨hal-00004755⟩