Meyer's signature cocycle and hyperelliptic fibrations

By H. Endo. 2000

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Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations (2004, methodology): “If the Lefschetz fibration is hyperelliptic, a local signature, which is a generalization of the σ-number [28] and the fractional signature [29] due to Matsumoto, was defined by the first author [12] and a method of computing signatures was established.”
Cohomological structure of the mapping class group and beyond (2005, background): “There are also various interesting works related to the class d1 such as Endo [14] and Morifuji [71] treating the hyperelliptic mapping class group, Kitano [54] as well as Hain and Reed [33].”
Lefschetz pencils and divisors in moduli space (2000, background): “The particular advantage of working with the hyperelliptic divisor is the well-known restriction on Lefschetz pencils giving rise to spheres with image contained inside it [7]:”
Problems on Mapping Class Groups And Related Topics (2006, methodology): “A result about homomorphisms between the mapping class groups of surfaces of different genera is due to Harvey and the author [14]: if g > h, then the image of any homomorphism Modg → Modh is trivial, with only one exception (in the case g = 2, the order of the image is at most 2).”
Monodromy substitutions and rational blowdowns (2010, background): “[4]) and the Euler characteristic of X( ) is 4g(4g − 1).”