INDEX THEOREMS ON MANIFOLDS WITH STRAIGHT ENDS.

Werner Ballmann (1, 2) , Jochen Brüning (3) , Gilles Carron (4)

1 Mathematisches Institut der Universität Bonn
2 MPI - Max-Planck-Institut für Mathematik
3 Institut für Mathematik [Berlin]
4 LMJL - Laboratoire de Mathématiques Jean Leray

We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.

Mots clés: Dirac operator; Fredholm type; non-parabolic; index

Domaines: Géométrie différentielle [math.DG]

Werner Ballmann, Jochen Brüning, Gilles Carron. INDEX THEOREMS ON MANIFOLDS WITH STRAIGHT ENDS.. Compositio Mathematica, 2012, 148, pp.1897-1968. ⟨hal-00534166v2⟩