We give an explicit formula for the signature of handlebody bundles over the circle interms 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.
Signature cocycle, handlebody group, mapping class groups
KUNO, YUSUKE and SATO, MASATOSHI
"The Meyer function on the handlebody group,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/1