Superconnections and Index Theory

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M. F. Atiyah and I. M. Singer, The index of elliptic operators I , Ann. Math. 87

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V. K. Patodi, Curvature and the eigenforms of the laplace operator , J. Differential Geometry 5

1971

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M. F. Atiyah, R. Bott, and V. K. Patodi, On the heat equation and the index theorem , Invent. Math. 19

1973

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P. Deligne, Théorie de Hodge. III , Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77

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M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry I , Math. Proc. Cambridge Philos. Soc. 77

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J. Cheeger and J. Simons, Differential characters and geometric invariants , Geometry and topology (College Park, Md., 1983/84), Lecture Notes in Math., vol. 1167, Springer, Berlin, 1985, pp. 50–80

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D. Quillen, Determinants of Cauchy-Riemann operators over a Riemann surface , AI 19

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by same author, Superconnections and the Chern character , Topology 24

1985

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J. M. Bismut and D. S. Freed, The analysis of elliptic families I: Metrics and connections , Commun. Math. Phys. 106

1986

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by same author, The analysis of elliptic families I​​ ​ I: Dirac operators, eta invariants, and the holonomy theorem of Witten , Commun. Math. Phys. 107

1986

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E. Getzler, A short proof of the local Atiyah-Singer index theorem , Topology 25

1986

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J.-M. Bismut, The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs , Inv. Mathematicae 83

1989

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P. Deligne and J. W. Morgan, Quantum fields and strings: A course for mathematicians , vol. 1, ch. 1, pp. 41–357, American Mathematical Society, 1999

1999

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by same author, Dirac charge quantization and generalized differential cohomology , Surveys in differential geometry, Surv. Differ. Geom., VII, Int. Press, Somerville, MA, 2000, pp. 129–194

2000

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N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators , Springer-Verlag, 2004

2004

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M. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory , J. Differential Geom. 70

2005

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D. S. Freed and G. W. Moore, Setting the quantum integrand of M-theory , Commun. Math. Phys. 263

2006

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