A GEOMETRIC APPROACH TO K-HOMOLOGY FOR LIE MANIFOLDS

Karsten Bohlen , Jean-Marie Lescure (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We prove that the computation of the Fredholm index for fully elliptic pseudodifferential operators on Lie manifolds can be reduced to the computation of the index of Dirac operators perturbed by smoothing operators. To this end we adapt to our framework ideas coming from Baum-Douglas geometric K-homology and in particular we introduce a notion of geometric cycles that can be classified into a variant of the famous geometric K-homology groups, for the specific situation here. We also define comparison maps between this geometric K-homology theory and relative K-theory.

Domaines: Algèbres d'opérateurs [math.OA]

Karsten Bohlen, Jean-Marie Lescure. A GEOMETRIC APPROACH TO K-HOMOLOGY FOR LIE MANIFOLDS. 2019. ⟨hal-02090537⟩