Direct image for some secondary K-theories
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 289-360. 
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     author = {Berthomieu, Alain},
     title = {Direct image for some secondary $K$-theories},
     booktitle = {From probability to geometry (I) - 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 = {289--360},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     mrnumber = {2642362},
     zbl = {1208.19005},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__289_0/}
}
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Berthomieu, Alain. Direct image for some secondary $K$-theories, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 289-360. http://www.numdam.org/item/AST_2009__327__289_0/

[1] M. F. Atiyah, V. K. Patodi & I. M. Singer - "Spectral asymmetry and Riemannian geometry. III", Math. Proc. Cambridge Philos. Soc. 79 (1976), p. 71-99. | DOI | MR | Zbl

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

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

[4] A. Berthomieu - "Proof of Nadel's conjecture and direct image for relative K-theory", Bull. Soc. Math. France 130 (2002), p. 253-307. | DOI | EuDML | Numdam | MR | Zbl

[5] A. Berthomieu & J.-M. Bismut - "Quillen metrics and higher analytic torsion forms", J. reine angew. Math. 457 (1994), p. 85-184. | EuDML | MR | Zbl

[6] J.-M. Bismut - "The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs", Invent. Math. 83 (1985), p. 91-151. | DOI | EuDML | MR | Zbl

[7] J.-M. Bismut, "Eta invariants, differential characters and flat vector bundles", Chinese Ann. Math. Ser. B 26 (2005), p. 15-44. | DOI | MR | Zbl

[8] J.-M. Bismut & J. Cheeger - "η-invariants and their adiabatic limits", J. Amer. Math. Soc. 2 (1989), p. 33-70. | MR | Zbl

[9] J.-M. Bismut, H. Gillet & C. Soulé - "Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott-Chern forms", Comm. Math. Phys. 115 (1988), p. 79-126. | DOI | MR | Zbl

[10] J.-M. Bismut & K. Köhler - "Higher analytic torsion forms for direct images and anomaly formulas", J. Algebraic Geom. 1 (1992), p. 647-684. | MR | Zbl

[11] J.-M. Bismut & J. Lott - "Flat vector bundles, direct images and higher real analytic torsion", J. Amer. Math. Soc. 8 (1995), p. 291-363. | DOI | MR | Zbl

[12] A. Borel - "Stable real cohomology of arithmetic groups", Ann. Sci. Ecole Norm. Sup. 7 (1974), p. 235-272. | DOI | EuDML | Numdam | MR | Zbl

[13] U. Bunke - "Index theory, eta forms, and Deligne cohomology", Mem. Amer. Math. Soc. 198 (2009). | MR | Zbl

[14] U. Bunke & T. Schick - "Smooth K-theory", Astérisque 328 (2010), p. 45-134. | Numdam | MR | Zbl

[15] 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

[16] X. Dai - "Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence", J. Amer. Math. Soc. 4 (1991), p. 265-321. | DOI | MR | Zbl

[17] J. L. Dupont - "Characteristic classes for flat bundles and their formulas", Topology 33 (1994), p. 575-590. | DOI | MR | Zbl

[18] M. Felisatti & F. Neumann - "Secondary theories for simplicial manifolds and classifying spaces", in Proceedings of the School and Conference in Algebraic Topology, Geom. Topol. Monogr., vol. 11, Geom. Topol. Publ., Coventry, 2007, p. 33-58. | MR | Zbl

[19] D. S. Freed - "Dirac charge quantization and generalized differential cohomology", in Surveys in differential geometry, Surv. Differ. Geom., VII, Int. Press, Somerville, MA, 2000, p.129-194. | MR | Zbl

[20] D. S. Freed & M. Hopkins - "On Ramond-Ramond fields and K-theory", J. High Energy Phys. 5 (2000), paper 44, 14. | MR | Zbl

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

[22] D. Husemoller - Fibre bundles, McGraw-Hill Book Co., 1966. | DOI | MR | Zbl

[23] D. L. Johnson - "Secondary characteristic classes and intermediate Jacobians", J. reine angew. Math. 347 (1984), p. 134-145. | EuDML | MR | Zbl

[24] D. L. Johnson,"Smooth moduli and secondary characteristic classes of analytic vector bundles", seemingly unpublished previous work to [23].

[25] F. W. Kamber & P. Tondeur - "Characteristic invariants of foliated bundles", Manuscripta Math. 11 (1974), p. 51-89. | DOI | EuDML | MR | Zbl

[26] M. Karoubi - "Homologie cyclique et K-théorie", Astérisque 149 (1987). | Numdam | MR | Zbl

[27] M. Karoubi, "Théorie générale des classes caractéristiques secondaires", K-Theory 4 (1990), p. 55-87. | DOI | MR | Zbl

[28] M. Karoubi, "Classes caractéristiques de fibrés feuilletés, holomorphes ou algébriques", in Proceedings of Conference on Algebraic Geometry and Ring Theory in honor of Michael Artin, Part II (Antwerp, 1992), vol. 8, 1994, p. 153-211. | MR | Zbl

[29] H. B. J. Lawson & M.-L. Michelsohn - Spin geometry, Princeton Mathematical Series, vol. 38, Princeton Univ. Press, 1989. | MR | Zbl

[30] J. Lott - " 𝐑/𝐙 index theory", Comm. Anal. Geom. 2 (1994), p. 279-311. | DOI | MR | Zbl

[31] X. Ma - "Functoriality of real analytic torsion forms", Israel J. Math. 131 (2002), p. 1-50. | DOI | MR | Zbl

[32] X. Ma & W. Zhang - "Eta-invariants, torsion forms and flat vector bundles", Math. Ann. 340 (2008), p. 569-624. | DOI | MR | Zbl

[33] R. R. Mazzeo & R. B. Melrose - "The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration", J. Differential Geom. 31 (1990), p. 185-213. | DOI | MR | Zbl

[34] R. B. Melrose & P. Piazza - "An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary", J. Differential Geom. 46 (1997), p. 287-334. | DOI | MR | Zbl

[35] A. M. Nadel - "Invariants for holomorphic vector bundles", Math. Ann. 309 (1997), p. 37-52. | DOI | MR | Zbl

[36] D. Poutriquet - "K-théorie des singularités coniques isolées", Ph.D. Thesis, Université Paul Sabatier, Toulouse, 2006.

[37] D. Quillen - "Superconnections and the Chern character", Topology 24 (1985), p. 89-95. | DOI | MR | Zbl