Summary
The purpose of this paper is to give two heat equation proofs of the Index Theorem of Atiyah-Singer for a family of Dirac operators.
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Bismut, JM. The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs. Invent Math 83, 91–151 (1986). https://doi.org/10.1007/BF01388755
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DOI: https://doi.org/10.1007/BF01388755