An index theorem for manifolds with boundary

Paulo Carrillo Rouse (1, 2) , Bertrand Monthubert (3, 4)

1 IMJ - Institut de Mathématiques de Jussieu
2 MPI-MiS - Max Planck Institute for Mathematics in the Sciences
3 LEP - Laboratoire Émile Picard
4 IMT - Institut de Mathématiques de Toulouse UMR5219

In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary.

Mots clés: index theory; manifolds with boundary; groupoids; K-theory.; K-theory

Domaines: K-théorie et homologie [math.KT]; Géométrie différentielle [math.DG]

Paulo Carrillo Rouse, Bertrand Monthubert. An index theorem for manifolds with boundary. 2009. ⟨hal-00382610⟩