Adiabatic limits of \(\eta \)-invariants and the Meyer functions (Q845760)

The authors aim to generalize an identity of Atiyah in which an automorphic form of higher dimension plays a role similar to the role of Dedekind eta function in Atiyah's study. They consider the signature cocycle of smooth theta divisors as a higher dimensional analogue of curves of genus 2, and they prove that the cohomology class of this cocycle vanishes rationally by constructing the Meyer function for smooth theta divisors. This rather long paper is clearly written and contains many interesting results with the help of methods of algebraic topology.