The Meyer function on the handlebody group

We give an explicit formula for the signature of handlebody bundles over the circle in terms of the homological monodromy. This gives a cobounding function of Meyer’s signature cocycle on the mapping class group of a 3-dimensional handlebody, i.e. the handlebody group. As an application, we give a topological interpretation for the generator of the first cohomology group of the hyperelliptic handlebody group.

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