Available in electronic format
Available in print format
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Twisted $ K$-theory and Poincaré duality

Author(s): Jean-Louis Tu
Journal: Trans. Amer. Math. Soc. 361 (2009), 1269-1278.
MSC (2000): Primary 46L80; Secondary 19K35
Posted: October 21, 2008
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Using methods of $ KK$-theory, we generalize Poincaré $ K$-duality to the framework of twisted $ K$-theory.


References:

1.
Atiyah, M. and Segal, G. Twisted $ K$-theory. Ukr. Mat. Visn. 1 (2004), no. 3, 287-330; translation in Ukr. Math. Bull. 1 (2004), no. 3, 291-334. MR 2172633 (2006m:55017)

2.
Brodzki, J., Mathai, V., Rosenberg, J. and Szabo, R. $ D$-branes, RR-fields and duality on noncommutative manifolds.

Comm. Math. Phys. 277 (2008), no. 3, 643-706. MR 2365448

3.
Bunke, U. and Schröder, I. Twisted $ K$-theory and TQFT. Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005, 33-80, Universitätsdrucke Göttingen, Göttingen, 2005. MR 2206878 (2007c:19008)

4.
Connes, A. and Skandalis, G. The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20, 1139-1183 (1984). MR 775126 (87h:58209)

5.
Carey, A.L. and Wang, B.L., Thom isomorphism and Push-forward map in twisted $ K$-theory. Preprint. arXiv:math/0512139

6.
Donovan, P. and Karoubi, M. Graded Brauer groups and K-theory with local coefficients. Pub. Math. IHES No. 38, p. 5-25 (1971). MR 0282363 (43:8075)

7.
Echterhoff, S., Emerson, H. and Kim, H.J. KK-theoretic duality for proper twisted actions. arXiv:math/0610044 Preprint.

8.
Freed, D., Hopkins, M. and Teleman, C. Twisted equivariant $ K$-theory with complex coefficients.

J. Topol. 1 (2008), no. 1, 16-44. MR 2365650

9.
Freed, D., Hopkins, M. and Teleman, C. Loop groups and twisted $ K$-theory II. ArXiv:math.AT/0206257.

10.
Hilsum, M. and Skandalis, G. Morphismes $ K$-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov. Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 3, 325-390. MR 925720 (90a:58169)

11.
Karoubi, M. Algèbres de Clifford et K-théorie. Ann. Sci. Ec. Norm. Sup., p. 161-270 (1968). MR 0238927 (39:287)

12.
Karoubi, M. Twisted K-theory, old and new. To appear in the Proceedings of the Valladolid conference (2007), European Mathematical Society.

13.
Kasparov, G. The operator $ K$-functor and extensions of $ C\sp{*} $-algebras. Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 3, 571-636, 719. MR 582160 (81m:58075)

14.
Kasparov, G. Equivariant $ KK$-theory and the Novikov conjecture. Inventiones Mathematicae, 91 (1988), 147-201. MR 918241 (88j:58123)

15.
Le Gall, P.Y. Théorie de Kasparov équivariante et groupoıdes. $ K$-Theory 16, 361-390 (1999). MR 1686846 (2000f:19006)

16.
Parker, E. M. The Brauer group of graded continuous trace $ C\sp *$-algebras. Trans. Amer. Math. Soc. 308 (1988), no. 1, 115-132. MR 946434 (89h:46080)

17.
Tu, J.L., Xu, P. and Laurent-Gengoux, C. Twisted $ K$-theory of differentiable stacks. Ann. Sci. Ens 37 (2004), no. 6, 841-910. MR 2119241 (2005k:58037)


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46L80, 19K35

Retrieve articles in all Journals with MSC (2000): 46L80, 19K35


Additional Information:

Jean-Louis Tu
Affiliation: Department of Mathematics, University Paul Verlaine-Metz, LMAM-CNRS UMR 7122, Ile du Saulcy, 57000 Metz, France
Email: tu@univ-metz.fr

DOI: 10.1090/S0002-9947-08-04706-5
PII: S 0002-9947(08)04706-5
Keywords: Twisted $K$-theory, $KK$-theory, Poincar\'e duality.
Received by editor(s): November 29, 2006
Posted: October 21, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google