Modular invariance and anomaly cancellation formulas in odd dimension

Abstract

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on $(4r-1)$ dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz operators on $(4r-1)$ dimensional spin manifolds and some congruent formulas on characteristic number for $(4r-1)$ dimensional spin${}^c$ manifolds.

16 pages. arXiv admin note: text overlap with arXiv:1109.5794, arXiv:0812.0201, arXiv:0811.4460; text overlap with arXiv:math/0605366 by other authors

References in corpus (4)

• Modular Forms and Generalized Anomaly Cancellation Formulas
• A note on modular forms and generalized anomaly cancellation formulas
• Modular Invariance and Twisted Anomaly Cancellations of Characteristic Numbers
• On the Witten Rigidity Theorem for Odd Dimensional Manifolds