A topological index theorem for manifolds with corners

Bertrand Monthubert (1, 2) , Victor Nistor (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LEP - Laboratoire Émile Picard
3 PSU - Department of Mathematics

We define an analytic index and prove a topological index theorem for a non-compact manifold $M_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M_0$ has an invertible perturbation $P+R$ by a lower order operator if an only if its analytic index vanishes. As an application, we determine the $K$-theory groups of groupoid $C^*$--algebras of manifolds with corners.

Mots clés: index theory; manifold with corners; Lie groupoid; pseudodifferential operator

Domaines: K-théorie et homologie [math.KT]; Algèbres d'opérateurs [math.OA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Bertrand Monthubert, Victor Nistor. A topological index theorem for manifolds with corners. Compositio Mathematica, 2012, 148 (2), pp.640-668. ⟨10.1112/S0010437X11005458⟩. ⟨hal-00007727⟩