Formules de Lichnerowicz et théorème de l’indice. (Lichnerowicz formulas and index theorem.). (French) Zbl 0648.58033

Bismut, Jean-Marie

Géométrie différentielle, Colloq. Géom. Phys., Paris/Fr. 1986, Trav. Cours 33, 11-31 (1988).

[For the entire collection see Zbl 0635.00010.]
In the first section of this paper the index theorem of M. F. Atiyah and I. M. Singer is proved by using probabilistic methods and Lichnerowicz formulas. In the second section the index theorem for families is proved by using localization formulas, superconnections of Levi-Civita-Quillen and \(\eta\)-invariant.

Reviewer: V.Deundjak

MSC:

58J20	Index theory and related fixed-point theorems on manifolds
60J65	Brownian motion
58J65	Diffusion processes and stochastic analysis on manifolds

Keywords:

Dirac operator; index theorem; probabilistic methods; superconnections

Citations:

Zbl 0635.00010