Celebratio Mathematica — Singer — Complete Bibliography

Complete Bibliography

Works connected to Jean-Michel Bismut

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V. Mathai, R. B. Melrose, and I. M. Singer: “The index of projective families of elliptic operators: The decomposable case,” pp. 255–296 in From probability to geometry, II: Volume in honor of the 60th birthday of Jean-Michel Bismut. Edited by X. Dai, R. Léandre, X. Ma, and W. Zhang. Astérisque 328. Société Mathématique de France (Paris), 2009. MR 2674880 Zbl 1207.19006 ArXiv 0809.0028 incollection

An index theory for projective families of elliptic pseudodifferential operators is developed under two conditions. First, that the twisting, i.e. Dixmier–Douady, class is in \[ H^2(X;\mathbb{Z}) \cup H^1(X;\mathbb{Z}) \subset H^3(X;\mathbb{Z}) \] and secondly that the 2-class part is trivialized on the total space of the fibration. One of the features of this special case is that the corresponding Azumaya bundle can be refined to a bundle of smoothing operators. The topological and the analytic ndex of a projective family of elliptic operators associated with the smooth Azumaya bundle both take values in twisted \( K \)-theory of the parameterizing space and the main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern–Weil theory.

Xianzhe Dai	Related
Xiaonan Ma	Related
Varghese Mathai	Related
Richard Burt Melrose	Related
Rémi Léandre	Related
Weiping Zhang	Related
Jean-Michel Bismut	Related