## The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas.(English)Zbl 0556.58027

In the first part of the article [ibid. 57, 56-99 (1984; Zbl 0538.58033)] the author gave a probabilistic proof of the Atiyah-Singer index theorem for classical elliptic complex and in this second part the Atiyah-Bott- Lefschetz fixed point formulas for elliptic spin-complexes are proved by using some probabilistic methods.
Reviewer: V.Deundjak

### MSC:

 58J20 Index theory and related fixed-point theorems on manifolds

Zbl 0538.58033
Full Text:

### References:

 [1] Atiyah, M.F; Bott, R; Atiyah, M.F; Bott, R, A Lefschetz fixed point formula for elliptic complexes, II, Ann. of math., Ann. of math., 88, 451-491, (1968) · Zbl 0167.21703 [2] Atiyah, M.F; Singer, I.M; Atiyah, M.F; Singer, I.M, The index of elliptic operators, II, Ann. of math., Ann. of math., 87, 546-604, (1968) · Zbl 0164.24301 [3] Bismut, J.M, Large deviations and the Malliavin calculus, () · Zbl 0537.35003 [4] Bismut, J.M, The Atiyah-Singer theorems: A probabilistic approach, I; the index theorem, J. funct. anal., 57, 56-99, (1984) · Zbl 0538.58033 [5] Gaveau, B, Principe de moindre action, propagation de la chaleur et estimées souselliptiques sur certains groupes nilpotents, Acta math., 139, 96-153, (1977) · Zbl 0366.22010 [6] Gilkey, P, Lefschetz fixed point formulas and the heat equation, (), 91-147 [7] Yor, M, Remarques sur une formule de P. Lévy, (), 343-346
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.