Even dimensional manifolds and generalized anomaly cancellation formulas
HTML articles powered by AMS MathViewer
- by Fei Han and Xiaoling Huang PDF
- Trans. Amer. Math. Soc. 359 (2007), 5365-5381 Request permission
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
- Luis Alvarez-Gaumé and Edward Witten, Gravitational anomalies, Nuclear Phys. B 234 (1984), no. 2, 269–330. MR 736803, DOI 10.1016/0550-3213(84)90066-X
- M. F. Atiyah, $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1967. Lecture notes by D. W. Anderson. MR 0224083
- M. F. Atiyah and F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc. 65 (1959), 276–281. MR 110106, DOI 10.1090/S0002-9904-1959-10344-X
- K. Chandrasekharan, Elliptic functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 281, Springer-Verlag, Berlin, 1985. MR 808396, DOI 10.1007/978-3-642-52244-4
- S. M. Finashin, A $\textrm {Pin}^-$-cobordism invariant and a generalization of the Rokhlin signature congruence, Algebra i Analiz 2 (1990), no. 4, 242–250 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 4, 917–924. MR 1080207
- Fei Han and Weiping Zhang, $\textrm {Spin}^c$-manifolds and elliptic genera, C. R. Math. Acad. Sci. Paris 336 (2003), no. 12, 1011–1014 (English, with English and French summaries). MR 1993972, DOI 10.1016/S1631-073X(03)00241-3
- Fei Han and Weiping Zhang, Modular invariance, characteristic numbers and $\eta$ invariants, J. Differential Geom. 67 (2004), no. 2, 257–288. MR 2153079
- F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
- Peter S. Landweber, Elliptic cohomology and modular forms, Elliptic curves and modular forms in algebraic topology (Princeton, NJ, 1986) Lecture Notes in Math., vol. 1326, Springer, Berlin, 1988, pp. 55–68. MR 970281, DOI 10.1007/BFb0078038
- Kefeng Liu, Modular invariance and characteristic numbers, Comm. Math. Phys. 174 (1995), no. 1, 29–42. MR 1372798
- Kefeng Liu and Wei Ping Zhang, Elliptic genus and $\eta$-invariant, Internat. Math. Res. Notices 8 (1994), 319 ff., approx. 9 pp.}, issn=1073-7928, review= MR 1289577, doi=10.1155/S1073792894000371,
- 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.
- Weiping Zhang, Spin$^c$-manifolds and Rokhlin congruences, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 7, 689–692 (English, with English and French summaries). MR 1245100
- Wei Ping Zhang, Circle bundles, adiabatic limits of $\eta$-invariants and Rokhlin congruences, Ann. Inst. Fourier (Grenoble) 44 (1994), no. 1, 249–270 (English, with English and French summaries). MR 1262887
- Weiping Zhang, Lectures on Chern-Weil theory and Witten deformations, Nankai Tracts in Mathematics, vol. 4, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. MR 1864735, DOI 10.1142/9789812386588
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
- Received by editor(s): September 5, 2005
- Published electronically: June 13, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 5365-5381
- MSC (2000): Primary 53C20, 57R20; Secondary 53C80, 11Z05
- DOI: https://doi.org/10.1090/S0002-9947-07-04214-6
- MathSciNet review: 2327034