#### Volume 14, issue 1 (2014)

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Gravitational anomaly cancellation and modular invariance

### Fei Han and Kefeng Liu

Algebraic & Geometric Topology 14 (2014) 91–113
##### Abstract

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $\left(4k+2\right)$–dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaumé and Witten in dimensions $2$, $6$ and $10$ [Nuclear Phys. B 234(2) (1984) 269–330] as special cases. In dimension $4k+1$, we derive anomaly cancellation formulas for index gerbes. In dimension $4k+3$, we obtain certain results about eta invariants, which are interesting in spectral geometry.

##### Keywords
gravitational anomaly cancellation, modular invariance
##### Mathematical Subject Classification 2010
Primary: 53C27, 53C80
##### Publication
Received: 14 May 2013
Revised: 6 June 2013
Accepted: 18 June 2013
Preview posted: 21 November 2013
Published: 9 January 2014
##### Authors
 Fei Han Department of Mathematics National University of Singapore Block S17, 10 Lower Kent Ridge Road Singapore 119076 Singapore Kefeng Liu Department of Mathematics University of California, Los Angeles 405 Hilgard Avenue Los Angeles, CA 90095 USA http://www.math.ucla.edu/~liu