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Heat Kernels and Dirac Operators by Nicole Berline, Ezra Getzler, and Michèle Vergne presents a comprehensive study of the interplay between heat kernels and Dirac operators on compact Riemannian manifolds. The authors provide accessible proofs of the Atiyah-Singer Index Theorem and its generalizations, utilizing an explicit geometric construction of the heat kernel associated with generalized Dirac operators.

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245: $a: Heat Kernels and Dirac Operators
245: $b:
082: $a:
100: $a: Nicole Berline & Ezra Getzler & Michèle Vergne
650: $a: Mathematics, Differential Geometry
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440: $v: 298
250: $b: Springer
250: $c: 2010
020: $a: 9780387533407
300: $a: 369