Smooth K-theory
From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 45-135. 
@incollection{AST_2009__328__45_0,
     author = {Bunke, Ulrich and Schick, Thomas},
     title = {Smooth $K$-theory},
     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 = {45--135},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {328},
     year = {2009},
     zbl = {1202.19007},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__328__45_0/}
}
TY  - CHAP
AU  - Bunke, Ulrich
AU  - Schick, Thomas
TI  - Smooth $K$-theory
BT  - From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut
AU  - Collectif
ED  - Dai Xianzhe
ED  - Léandre Rémi
ED  - Xiaonan Ma
ED  - Zhang Weiping
T3  - Astérisque
PY  - 2009
SP  - 45
EP  - 135
IS  - 328
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2009__328__45_0/
LA  - en
ID  - AST_2009__328__45_0
ER  - 
%0 Book Section
%A Bunke, Ulrich
%A Schick, Thomas
%T Smooth $K$-theory
%B From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut
%A Collectif
%E Dai Xianzhe
%E Léandre Rémi
%E Xiaonan Ma
%E Zhang Weiping
%S Astérisque
%D 2009
%P 45-135
%N 328
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2009__328__45_0/
%G en
%F AST_2009__328__45_0
Bunke, Ulrich; Schick, Thomas. Smooth $K$-theory, dans From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 45-135. http://www.numdam.org/item/AST_2009__328__45_0/

[1] M. F. Atiyah, R. Bott & A. Shapiro - "Clifford modules", Topology 3 (1964), p. 3-38. | DOI | Zbl

[2] M. F. Atiyah, V. K. Patodi & I. M. Singer - "Spectral asymmetry and Riemannian geometry. I", Math. Proc. Cambridge Philos. Soc. 77 (1975), p. 43-69. | DOI | Zbl

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

[4] S. Baaj & P. Julg - "Théorie bivariante de Kasparov et opérateurs non bornés dans les C*-modules hilbertiens", C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), p. 875-878. | Zbl

[5] P. Baum & R. G. Douglas - "Index theory, bordism, and K-homology", in Operator algebras and K-theory (San Francisco, Calif., 1981), Contemp. Math., vol. 10, Amer. Math. Soc., 1982, p. 1-31. | Zbl

[6] P. Baum, N. Higson & T. Schick - "On the equivalence of geometric and analytic K-homology", Pure Appl. Math. Q. 3 (2007), p. 1-24. | DOI | Zbl

[7] N. Berline, E. Getzler & M. Vergne - Heat kernels and Dirac operators, Grundlehren Text Editions, Springer, 2004. | Zbl

[8] A. Berthomieu - "Direct image for multiplicative and relative K-theories from transgression of the families index theorem, part 1", preprint arXiv:math.DG/0611281.

[9] A. Berthomieu, "Direct image for multiplicative and relative K-theories from transgression of the families index theorem, part 2", preprint arXiv:math.DG/0703916.

[10] 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 | Zbl

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

[12] J.-M. Bismut & J. Cheeger - "Families index for manifolds with boundary, super-connections, and cones. I. Families of manifolds with boundary and Dirac operators", J. Funct. Anal. 89 (1990), p. 313-363. | DOI | Zbl

[13] J.-M. Bismut & J. Cheeger, "Families index for manifolds with boundary, superconnections and cones. II. The Chern character", J. Funct. Anal. 90 (1990), p. 306-354. | DOI | Zbl

[14] J.-M. Bismut & J. Cheeger, "Remarks on the index theorem for families of Dirac operators on manifolds with boundary", in Differential geometry, Pitman Monogr. Surveys Pure Appl. Math., vol. 52, Longman Sci. Tech., 1991, p. 59-83. | Zbl

[15] 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 | Zbl

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

[17] U. Bunke - "A K-theoretic relative index theorem and Callias-type Dirac operators", Math. Ann. 303 (1995), p. 241-279. | DOI | EuDML | Zbl

[18] U. Bunke, "On the functoriality of Lott's secondary analytic index", K-Theory 25 (2002), p. 51-58. | DOI | Zbl

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

[20] U. Bunke, M. Kreck & T. Schick - "A geometric description of smooth cohomology", Ann. Math. Blaise Pascal 17 (2010), p. 1-16. | DOI | EuDML | Numdam | Zbl

[21] U. Bunke & X. Ma - "Index and secondary index theory for flat bundles with duality", in Aspects of boundary problems in analysis and geometry, Oper. Theory Adv. Appl., vol. 151, Birkhäuser, 2004, p. 265-341. | Zbl

[22] U. Bunke & T. Schick - "Uniqueness of smooth extensions of generalized cohomology theories", J. Topology 3 (2010), p. 110-156. | DOI | Zbl

[23] U. Bunke, T. Schick, I. Schröder & M. Wiethaup - "Landweber exact formal group laws and smooth cohomology theories", Algebr. Geom. Topol. 9 (2009), p. 1751-1790. | DOI | Zbl

[24] 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. | Zbl

[25] J. L. Dupont & R. Ljungmann - "Integration of simplicial forms and Deligne cohomology", Math. Scand. 97 (2005), p. 11-39. | DOI | MR | Zbl

[26] 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

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

[28] D. S. Freed & R. B. Melrose - "A mod k index theorem", Invent. Math. 107 (1992), p. 283-299. | DOI | EuDML | MR | Zbl

[29] K. Gomi - "Differential characters and the Steenrod squares", Adv. Stud. Pure Math. 52 (2008), p. 297-308. | MR | Zbl

[30] K. Gomi & Y. Terashima - "A fiber integration formula for the smooth Deligne cohomology", Int. Math. Res. Not. 2000 (2000), p. 699-708. | DOI | MR | Zbl

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

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

[33] M. Karoubi, "Sur la K-théorie multiplicative", in Cyclic cohomology and noncommutative geometry (Waterloo, ON, 1995), Fields Inst. Commun., vol. 17, Amer. Math. Soc., 1997, p. 59-77. | MR | Zbl

[34] G. G. Kasparov - "The operator K-functor and extensions of C * -algebras", Izv. Akad. Nauk SSSR Ser. Mat 44 (1980), p. 571-636, 719. | MR | Zbl

[35] M. Köhler - Die Integrationsabbildung in Deligne Kohomologie und Verknüpfung von Faserbündeln, Master's Thesis, Fachbereich Mathematik, Georg-August-Universität Göttingen, 2007.

[36] G. Laures - "The topological q-expansion principle", Topology 38 (1999), p. 387-425. | DOI | MR | Zbl

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

[38] J. Lott, "Secondary analytic indices", in Regulators in analysis, geometry and number theory, Progr. Math., vol. 171, Birkhäuser, 2000, p. 231-293. | DOI | MR | Zbl

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

[40] R. B. Melrose & P. Piazza - "Families of Dirac operators, boundaries and the b-calculus", J. Differential Geom. 46 (1997), p. 99-180. | DOI | MR | Zbl

[41] 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

[42] R. B. Melrose & F. Rochon - "Periodicity and the determinant bundle", Comm. Math. Phys. 274 (2007), p. 141-186. | DOI | MR | Zbl

[43] O. Pekonen - "A K-theoretic approach to Chern-Cheeger-Simons invariants", in Proceedings of the Winter School "Geometry and Physics" (SRNI, 1991), vol. 30, 1993, p. 27-34. | EuDML | MR | Zbl

[44] J. Simons & D. Sullivan - "Axiomatic characterization of ordinary differential cohomology", J. Topology 1 (2008), p. 45-56. | DOI | MR | Zbl

[45] R. E. Stong - Notes on cobordism theory, Mathematical notes, Princeton Univ. Press, 1968. | MR | Zbl