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Consistent and covariant Lorentz and diffeomorphism anomalies areinvestigated in terms of the geometry of the universal bundle for gravity. Thisbundle is explicitly constructed and its geometrical structure will be studied.By means of the local index theorem for families of Bismut and Freed theconsistent gravitational anomalies are calculated. Covariant gravitationalanomalies are shown to be related with secondary characteristic classes of theuniversal bundle and a new set of descent equations which also contains thecovariant Schwinger terms is derived. The relation between consistent andcovariant anomalies is studied. Finally a geometrical realization of thegravitational BRS, anti-BRS transformations is presented which enables theformulation of a kind of covariance condition for covariant gravitationalanomalies.Comment: 32 pages, LMU-TPW 93-16, typeset by amste

Universal bundle for gravity, local index theorem, and covariant gravitational anomalies