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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

Citations:

Zbl 0538.58033
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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
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