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Modular invariance and twisted cancellations of characteristic numbers
Authors:
Qingtao Chen and Fei Han
Journal:
Trans. Amer. Math. Soc. 361 (2009), 1463-1493
MSC (2000):
Primary 58J26; Secondary 58J20
Posted:
October 17, 2008
MathSciNet review:
2457406
Full-text PDF
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Additional Information
Abstract: By studying modular invariance properties of some characteristic forms, which are related to elliptic genera, we obtain twisted cancellation formulas for characteristic forms. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin manifolds. In particular, we obtain twisted Rokhlin congruences for  dimensional spin manifolds.
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- M. F. Atiyah and F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds. Bull. Amer. Math. Soc. 65 (1959), 276-281. MR 0110106 (22:989)
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- M. F. Atiyah and I. M. Singer, The index of elliptic operators, III, Ann. Math. 87 (1968), 546-604. MR 0236952 (38:5245)
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- K. Chandrasekharan, Elliptic Functions. Springer-Verlag, 1985. MR 808396 (87e:11058)
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 invariants. Journal of Differential Geometry. 67 (2004), 257-288. MR 2153079 (2006k:58038)
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Additional Information
Qingtao Chen
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720-3840
Email:
chenqtao@math.berkeley.edu
Fei Han
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720-3840
Address at time of publication:
Department of Mathematics, Stanford University, Stanford, California 94305-2125
Email:
feihan@math.berkeley.edu
DOI:
http://dx.doi.org/10.1090/S0002-9947-08-04703-X
PII:
S 0002-9947(08)04703-X
Received by editor(s):
February 16, 2007
Posted:
October 17, 2008
Article copyright:
© Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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