### 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^{c} manifolds. In particular, we obtain twisted Rokhlin congruences for 8k + 4 dimensional spin^{c} manifolds.

Original language | English (US) |
---|---|

Pages (from-to) | 1463-1493 |

Number of pages | 31 |

Journal | Transactions of the American Mathematical Society |

Volume | 361 |

Issue number | 3 |

State | Published - Mar 1 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*361*(3), 1463-1493.

**Modular invariance and twisted cancellations of characteristic numbers.** / Chen, Qingtao; Han, Fei.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 361, no. 3, pp. 1463-1493.

}

TY - JOUR

T1 - Modular invariance and twisted cancellations of characteristic numbers

AU - Chen, Qingtao

AU - Han, Fei

PY - 2009/3/1

Y1 - 2009/3/1

N2 - 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 spinc manifolds. In particular, we obtain twisted Rokhlin congruences for 8k + 4 dimensional spinc manifolds.

AB - 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 spinc manifolds. In particular, we obtain twisted Rokhlin congruences for 8k + 4 dimensional spinc manifolds.

UR - http://www.scopus.com/inward/record.url?scp=77950521737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950521737&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77950521737

VL - 361

SP - 1463

EP - 1493

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -