Abstract
We discuss the use of the family's index theorem in the study of gravitational anomalies. The geometrical framework required to apply the family's index theorem is presented and the relation to gravitational anomalies is discussed. We show how physics necessitates the introduction of the notion oflocal cohomology which is distinct from the ordinary topological cohomology. The recent results of Alvarez-Gaumé and Witten are derived by using the family's index theorem.
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Communicated by R. Stora
This work was supported in part by the National Science Foundation under Contracts PHY81-18547 and MCS80-23356; and by the Director, Office of High Energy and Nuclear Physics of the US Department of Energy under Contracts DE-AC03-76SF00098 and AT0380-ER10617
Alfred P. Sloan Foundation Fellow
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Alvarez, O., Singer, I.M. & Zumino, B. Gravitational anomalies and the family's index theorem. Commun.Math. Phys. 96, 409–417 (1984). https://doi.org/10.1007/BF01214584
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DOI: https://doi.org/10.1007/BF01214584