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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Even dimensional manifolds and generalized anomaly cancellation formulas

Author(s): Fei Han; Xiaoling Huang
Journal: Trans. Amer. Math. Soc. 359 (2007), 5365-5381.
MSC (2000): Primary 53C20, 57R20; Secondary 53C80, 11Z05
Posted: June 13, 2007
MathSciNet review: 2327034
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We give a direct proof of a cancellation formula raised by Han and Zhang (2004) on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among these cancellation formulas are discussed.


References:

1.
L. Alvarez-Gaumé and E. Witten, Gravitational anomalies. Nucl. Phys. B234 (1983), 269-330. MR 736803 (85j:81062)

2.
M. F. Atiyah, $ K$-theory. Benjamin, New York, 1967. MR 0224083 (36:7130)

3.
M. F. Atiyah and F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds. Bull. Amer. Math. Soc. 65 (1959), 276-281. MR 0110106 (22:989)

4.
K. Chandrasekharan, Elliptic Functions. Springer-Verlag, 1985. MR 808396 (87e:11058)

5.
S. M. Finashin, A Pin$ ^-$-cobordism invariant and a generalization of Rokhlin signature congruence. Leningrad Math. J. 2 (1991), 917-924. MR 1080207 (91i:57016)

6.
F. Han and W. Zhang, Spin$ ^{c}$-manifold and elliptic genera. C. R. Acad. Sci. Paris, S$ \acute{e}$rie I. 336 (2003), 1011-1014. MR 1993972 (2004j:58024)

7.
F. Han and W. Zhang, Modular invariance, characteristic numbers and $ \eta$ invariants. Journal of Differential Geometry. 67 (2004), 257-288. MR 2153079 (2006k:58038)

8.
F. Hirzebruch, Topological Methods in Algebraic Geometry. Springer-Verlag, 1966. MR 0202713 (34:2573)

9.
P. S. Landweber, Elliptic cohomology and modular forms. in Elliptic Curves and Modular Forms in Algebraic Topology, pp. 55-68. Ed. P. S. Landweber. Lecture Notes in Mathematics Vol. 1326, Springer-Verlag (1988). MR 970281

10.
K. Liu, Modular invariance and characteristic numbers. Commun. Math. Phys. 174 (1995), 29-42. MR 1372798 (96m:57034)

11.
K. Liu and W. Zhang, Elliptic genus and $ \eta$-invariants. Inter. Math. Res. Notices No. 8 (1994), 319-328. MR 1289577 (96b:57030)

12.
S. Ochanine, Signature modulo 16, invariants de Kervaire généralisés et nombres caractéristiques dans la $ K$-théorie réelle. Mémoire Soc. Math. France, Tom. 109 (1987), 1-141.

13.
W. Zhang, Spin$ ^c$-manifolds and Rokhlin congruences. C. R. Acad. Sci. Paris, Série I, 317 (1993), 689-692. MR 1245100 (94i:57042)

14.
W. Zhang, Circle bundles, adiabatic limits of $ \eta$-invariants and Rokhlin congruences. Ann. Inst. Fourier 44 (1994), 249-270. MR 1262887 (95h:58127)

15.
W. Zhang, Lectures on Chern-Weil Theory and Witten Deformations. Nankai Tracts in Mathematics Vol. 4, World Scientific, Singapore, 2001. MR 1864735 (2002m:58032)


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Additional Information:

Fei Han
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: feihan@math.berkeley.edu

Xiaoling Huang
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: xiaoling@math.ucsb.edu

DOI: 10.1090/S0002-9947-07-04214-6
PII: S 0002-9947(07)04214-6
Received by editor(s): September 5, 2005
Posted: June 13, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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