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Toroidal orbifolds, gerbes and group cohomology
Authors:
Alejandro Adem and Jianzhong Pan
Journal:
Trans. Amer. Math. Soc. 358 (2006), 3969-3983
MSC (2000):
Primary 20J06
Posted:
April 11, 2006
MathSciNet review:
2219005
Full-text PDF Free Access
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Abstract: In this paper we compute the integral cohomology of certain semi-direct products of the form  , arising from a linear  action on the  -torus, where  is a finite group. The main application is the complete calculation of torsion gerbes for six-dimensional examples arising in string theory.
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(2002i:81186)
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J. (2) 45 (1993), no. 4, 535–537. MR 1245720
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- 1.
- Adem, A.,
 actions on  , Trans. Amer. Math. Soc. 300 (1987), no. 2, 791-809. MR 0876479 (88b:57037)
- 2.
- Adem, A. and Milgram, R.J., Cohomology of finite groups, Grundlehren der Mathematischen Wissenschaften 309, Springer-Verlag, Berlin, 1994. MR 1317096 (96f:20082)
- 3.
- de Boer, J., Dijkgraaf, R., Hori, K., Keurentjes, A., Morgan, J., Morrison, D. and Sethi, S., Triples, Fluxes, and Strings, Adv. Theor. Math. Phys. 4 (2000), no. 5, 995-1186. MR 1868756 (2002i:81186)
- 4.
- Brady, T., Free resolutions for semi-direct products, Tohoku Math. J. (2) 45 (1993), no. 4, 535-537. MR 1245720 (94f:20096)
- 5.
- Brown, K., Cohomology of groups, Grad. Texts in Mathematics 87 Springer-Verlag, New York, 1982. MR 0672956 (83k:20002)
- 6.
- Erler, J. and Klemm, A., Comment on the generation number in orbifold compactifications, Comm. Math. Phys. 153 (1993), 579-604. MR 1218933 (94i:32044)
- 7.
- Evens, L., Cohomology of groups, Oxford Mathematical Monographs, Oxford University Press (1991). MR 1144017 (93i:20059)
- 8.
- Joyce, D., Deforming Calabi-Yau orbifolds, Asian J. Math. 3 (1999), no. 4, 853-867.MR 1797581 (2001i:14004)
- 9.
- Lupercio, E. and Uribe, B., Gerbes over orbifolds and twisted K-theory, Comm. Math. Phys. 245 (2004), 449-489. MR 2045679 (2005m:53035)
- 10.
- Ruan, Y., Discrete torsion and twisted orbifold cohomology, J. Symplectic Geometry 2 (2003), 1-24. MR 2128387
- 11.
- Vafa, C. and Witten, E., On orbifolds with discrete torsion, J. Geom. Phys. 15 (1995), no. 3, 189-214. MR 1316330 (95m:81190)
- 12.
- Vafa, C., Modular invariance and discrete torsion on orbifolds, Nuclear Phys. B 273 (1986), no. 3-4, 592-606. MR 0850976 (87j:81232)
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Additional Information
Alejandro Adem
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Address at time of publication:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
Email:
adem@math.wisc.edu, adem@math.ubc.ca
Jianzhong Pan
Affiliation:
Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China
Email:
pjz@math03.math.ac.cn
DOI:
http://dx.doi.org/10.1090/S0002-9947-06-04017-7
PII:
S 0002-9947(06)04017-7
Keywords:
Orbifolds,
gerbes,
group cohomology
Received by editor(s):
June 10, 2004
Posted:
April 11, 2006
Additional Notes:
The first author was partially supported by the NSF, and the second author was partially supported by NSFC project 19701032
Article copyright:
© Copyright 2006 American Mathematical Society
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