High Energy Phys. Melrose - " A mod k index theorem ", Invent. Gomi - " Differential characters and the Steenrod squares ", Adv. Pure Math. Terashima - " A fiber integration formula for the smooth Deligne cohomology ", Int. Singer - " Quadratic functions in geometry, topology, and M-theory ", J. Differential Geom. Numdam MR Zbl Mat 44 , p. Laures - " The topological q -expansion principle ", Topology 38 , p.

Lott , " Secondary analytic indices ", in Regulators in analysis, geometry and number theory, Progr. Zhang - " Eta-invariants, torsion forms and flat vector bundles ", Math. Piazza - " Families of Dirac operators, boundaries and the b-calculus ", J. Piazza , " An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary ", J. Rochon - " Periodicity and the determinant bundle ", Comm. Sullivan - " Axiomatic characterization of ordinary differential cohomology ", J. Topology 1 , p. Stong - Notes on cobordism theory , Mathematical notes, Princeton Univ.

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Between and. Smooth K -theory. Bunke, Ulrich ; Schick, Thomas. The full text of recent articles is available to journal subscribers only. Lott - " Flat vector bundles, direct images and higher real analytic torsion ", J. Brylinski - Loop spaces, characteristic classes and geometric quantization , Progress in Math. Bunke , " On the functoriality of Lott's secondary analytic index ", K -Theory 25 , p. Bunke , " Index theory, eta forms, and Deligne cohomology ", Mem. Bunke , M.

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Bunke , T. Schick , I. Wiethaup - " Landweber exact formal group laws and smooth cohomology theories ", Algebr. Simons - " Differential characters and geometric invariants ", in Geometry and topology College Park, Md. Ljungmann - " Integration of simplicial forms and Deligne cohomology ", Math. Article MR Zbl Freed - " Dirac charge quantization and generalized differential cohomology ", in Surveys in differential geometry, Surv. Press, Somerville, MA, , p.

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MR Zbl High Energy Phys. Melrose - " A mod k index theorem ", Invent. Gomi - " Differential characters and the Steenrod squares ", Adv.

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Metric properties are also studied. This needs to revisit the construction of -forms in the case where the direct image is provided by the vertical Euler de Rham operator. Double submersions are also studied to establish some functoriality properties of these direct images. Keywords: Relative -theory, multiplicative -theory, smooth -theory, local families index, Chern-Simons, direct image, pushforward Class.