On the heat equation and the index theorem

@article{Atiyah1973OnTH,
  title={On the heat equation and the index theorem},
  author={Michael Francis Atiyah and Raoul Bott and V. K. Patodi},
  journal={Inventiones mathematicae},
  year={1973},
  volume={19},
  pages={279-330}
}
The main error occurs on page 306 where it is implicitly assumed that the coefficients of the two operators A*A and AA* (associated to the signature operator A) are polynomial functions in the gij, their derivatives and (det g)-l . As we shall show later this is not quite t r u e t h e coefficients also involve d ] f ~ and the inverses of the principal minors of the matrix gu" Thus the form m in (5.1) is not a regular invariant of the metric in the sense of w 2, and so the Gilkey Theorem as… Expand
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