The index of projective families of elliptic operators: the decomposable case
From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 255-296.
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     author = {Mathai, Varghese and Melrose, Richard B. and Singer, Isadore M.},
     title = {The index of projective families of elliptic operators: the decomposable case},
     booktitle = {From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {255--296},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {328},
     year = {2009},
     mrnumber = {2674880},
     zbl = {1207.19006},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2009__328__255_0/}
}
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Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. The index of projective families of elliptic operators: the decomposable case, dans From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 255-296. http://archive.numdam.org/item/AST_2009__328__255_0/

[1] P. Albin & R. B. Melrose - "Relative Chern character, boundaries and index formulæ", preprint arXiv:0808.0183. | MR | Zbl

[2] O. Alvarez, I. M. Singer & B. Zumino - "Gravitational anomalies and the family's index theorem", Comm. Math. Phys. 96 (1984), p. 409-417. | DOI | MR | Zbl

[3] M. Atiyah & F. Hirzebruch - "Riemann-Roch theorems for differentiable manifolds", Bull. Amer. Math. Soc. 65 (1959), p. 276-281. | DOI | MR | Zbl

[4] M. Atiyah & G. Segal - "Twisted K-theory and cohomology", in Inspired by S. S. Chern, Nankai Tracts Math., vol. 11, World Sci. Publ., Hackensack, NJ, 2006, p. 5-43. | DOI | MR | Zbl

[5] M. Atiyah & I. M. Singer - "The index of elliptic operators. IV", Ann. of Math. 93 (1971), p. 119-138. | DOI | MR | Zbl

[6] M. Atiyah & I. M. Singer, "Dirac operators coupled to vector potentials", Proc. Nat. Acad. Sci. U.S.A. 81 (1984), p. 2597-2600. | DOI | MR | Zbl

[7] N. Berline, E. Getzler & M. Vergne - Heat kernels and Dirac operators, Grund. Math. Wiss., vol. 298, Springer, 1992. | MR | Zbl

[8] P. Bouwknegt, J. Evslin & V. Mathai - "T-duality: topology change from H -flux", Comm. Math. Phys. 249 (2004), p. 383-415. | DOI | MR | Zbl

[9] J.-L. Brylinski - Loop spaces, characteristic classes and geometric quantization, Progress in Mathematics, vol. 107, Birkhäuser, 1993. | MR | Zbl

[10] A. L. Carey & B.-L. Wang - "Thom isomorphism and push-forward map in twisted K-theory", J. K-Theory 1 (2008), p. 357-393. | MR | Zbl

[11] J. Cheeger - "Multiplication of differential characters", in Symposia Mathematica, Vol. XI (Convegno di Geometria, INDAM, Rome, 1972), Academic Press, 1973, p. 441-445. | MR | Zbl

[12] J. Cheeger & J. Simons - "Differential characters and geometric invariants", in Geometry and topology (College Park, Md., 1983/84), Lecture Notes in Math., vol. 1167, Springer, 1985, p. 50-80. | MR | Zbl

[13] B. Fedosov - Deformation quantization and index theory, Mathematical Topics, vol. 9, Akademie Verlag, 1996. | MR | Zbl

[14] D. S. Freed - "Determinants, torsion, and strings", Comm. Math. Phys. 107 (1986), p. 483-513. | DOI | MR | Zbl

[15] A. Grigis & J. Sjöstrand - Microlocal analysis for differential operators, London Mathematical Society Lecture Note Series, vol. 196, Cambridge University Press, 1994. | MR | Zbl

[16] J. Harer - "The second homology group of the mapping class group of an orientable surface", Invent. Math. 72 (1983), p. 221-239. | DOI | EuDML | MR | Zbl

[17] M. J. Hopkins & I. M. Singer - "Quadratic functions in geometry, topology, and M-theory", J. Differential Geom. 70 (2005), p. 329-452. | DOI | MR | Zbl

[18] L. Hörmander - "Fourier integral operators. I", Acta Math. 127 (1971), p. 79-183. | DOI | MR | Zbl

[19] S. Johnson - "Constructions with bundle gerbes", Ph.D. Thesis, University of Adelaide, 2003, arXiv:math/0312175.

[20] V. Mathai, R. B. Melrose & I. M. Singer - "The index of projective families of elliptic operators", Geom. Topol. 9 (2005), p. 341-373. | DOI | EuDML | MR | Zbl

[21] R. B. Melrose - "From microlocal to global analysis", MIT lecture notes http://math.mit.edu/~rbm/18.199-S08/, 2008.

[22] S. Morita - Geometry of characteristic classes, Translations of Mathematical Monographs, vol. 199, Amer. Math. Soc., 2001. | MR | Zbl

[23] M. K. Murray - "Bundle gerbes", J. London Math. Soc. 54 (1996), p. 403-416. | DOI | MR | Zbl

[24] M. K. Murray, "An introduction to bundle gerbes", arXiv:0712.1651. | DOI | MR | Zbl