On Meyer's function of hyperelliptic mapping class groups

Abstract

In this paper, we consider Meyer's function of hyperelliptic mapping class groups of orientable closed surfaces and give certain explicit formulae for it. Moreover we study geometric aspects of Meyer's function, and relate it to the $\eta \text{-}$ invariant of the signature operator and Morita's homomorphism, which is the core of the Casson invariant of integral homology 3-spheres.