Gerbes over Orbifolds and Twisted K-Theory

Communications in Mathematical Physics

Volumn 245, Issue 3, 2004, Pages 449-489

  Lupercio, Ernesto ^a   Uribe, Bernardo ^b  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842434508     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-1035-x     Document Type: Review

References (35)

1. Adem, A.,Ruan, Y: Twisted orbifold K-theory. Commun. Math. Phys. 237(3), 533-556 (2003) MR 1 993 337
2. Atiyah, M.: K-Theory Past and Present. arXiv:math.KT/0012213
3. Behrend, K., Edidin, D., Fantechi, B., Fulton, W., Göttsche, L., Kresch, A.: Introduction to Stacks. In preparation
4. Bouwknegt, P., Carey, A.L., Mathai, V., Murray, M.K., Stevenson, D.: Twisted K-theory and K-theory of bundle gerbes. Commun. Math. Phys. 228(1), 17-45 (2002) MR 2003g:58049
5. Brylinski, J.-L.: Loop spaces characteristic classes and geometric quantization. Progress in Mathematics 107. Boston, MA: Birkhäuser Boston, Inc., 1993
6. Carey, A.L., Mickelsson, J.: The universal gerbe Dixmier-Douady class and gauge theory. Lett. Math. Phys. 59(1), 47-60 (2002) MR 2003e:58048
7. Chen, W.: A Homotopy Theory of Orbispaces. (2001) arXivmath.AT/0102020
8. Chen, W., Ruan, Y.: Orbifold Quantum Cohomology. (2000) arXiv:math.AG/0005198
9. Cohen, R.L., Jones, J.D.S., Segal, G.B.: Floer's infinite-dimensional Morse theory and homotopytheory. In: The Floer Memorial Volume, Basel: Birkhäuser, 1995, pp. 297-325
10. Crainic, M., Moerdijk, I.: A homology theory forétale groupoids. J. Reine Angew. Math. 521, 25-46 (2000)
11. Donovan, P., Karoubi, M.: Graded Brauer Groups and K-theory. IHES 38 (1970)
12. Freed, D.: The Verlinde algebra is twisted equivariant K-theory. arXiv:math.RT/0101038
13. Giraud, J.: Cohomologie non Abéliene. Berlin-Heidelberg-New York: Springer-Verlag, 1971
14. Grothendieck, A.: Dix exposés sur la cohomologie des schémas. Amsterdam: North Holland, 1968
15. Hitchin, N.: Lectures Notes on Special Lagrangian Submanifolds. (1999) arXiv:math.DG/9907034
16. Lupercio, E., Uribe, B.: Holonomy for grebes over orbifolds. arXiv:math.AT/0307114
17. Lupercio, E., Uribe, B.: Deligne Cohomology for Orbifolds Discrete Torsion and B-fields. In: Geometric and Topological methods for Quantum Field Theory, Singapore: World Scientific, 2002
18. Lupercio, E., Uribe, B.: Loop groupoids, gerbes, and twisted sectors on orbifolds. In: Orbifolds in mathematics and physics (Madison WI 2001), Contemp. Math. Vol. 310, Providence RI: Am. Math. Soc., 2002, 163-184 MR 1 950 946
19. May, P.: Simplicial Objects in Algebraic Topology. Van Nostrand Mathematical Studies 11, Princeton N.J.: D. Van Nostrand Co. Inc., 1967
20. Moerdijk, I.: Calssifying topos and foliations. Ann. Inst. Fourier 41, 189-209 (1991)
21. Moerdijk, I.: Proof of a conjecture of A. Haefiger. Topology 37(4), 735-741 (1998)
22. Moerdijk, I.: Orbifolds as groupoids: an introduction. In: Orbifolds in mathematics and physics (Madison, WI, 2001), Contemp. Math., Vol. 310, Providence, RI: Am. Math. Soc. (2002), pp. 205-222 MR 1 950 948
23. Moerdijk, I., Pronk, D.A.: Orbifolds sheaves and groupoids. K-Theory 12(1), 3-21 (1997)
24. Moerdijk, I., Pronk, D.A.: Simplicial cohomology of orbifolds. Indag. Math. (N.S.) 10(2), 403-416 (1999)
25. Murray, M.K.: Bundle Gerbes. J. Lond. Math. Soc. 54(2), 403-416 (1996)
26. Murray, M.K., Stevenson, D.: Bundle Gerbes. Stable isomorphism and local theory. J. Lond. Math. Soc. 62(2), 925-937 (2000)
27. Pressley, A., Segal, G.: Loop groups. New York: The Clarendon Press Oxford University Press, Oxford Science Publications, 1986
28. Rosenberg, J.: Continuous trace C*-algebras from the bundle theoretic point of view. J. Aust. Math. Soc. A47, 368 (1989)
29. Ruan, Y.: Stringy geometry and topology of orbifolds. In: Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000), Contemp. Math. Vol. 312, Providence RI: Am. Math. Soc. 2002, pp. 187-233 MR 1 941 583
30. Satake, I.: The Gauss -Bonet theorem for V-manifolds. J. Math. Soc. Japan 9, 464-492 (1957)
31. Segal, G.: Classifying spaces and spectral sequences. Inst. Hautes Etudes Sci. Publ. Math. 34, 105-112 (1968)
32. Segal, G.: Fredholm complexes. Quart. J. Math. Oxford Ser. 21(2), 385-402 (1970)
33. Segal, G.: Categories and cohomology theories. Topology 13, 292-312 (1974)
34. Thurston, W.: Three-dimensional geometry and topology. Vol. 1. Princeton Mathematical Series 35. Princeton NJ: Princeton University Press, 1997
35. Witten, E.: D-branes and K-theory. J. High Energy Phys. 12(19), pp. 41 (1998) (electronic). MR 2000e:81151