A twisted first homology group of the handlebody mapping class group

25 Feb 2015 · Ishida Tomohiko, Sato Masatoshi ·

Let $H_{g}$ be a 3-dimensional handlebody of genus $g$. We determine the twisted first homology group of the mapping class group of $H_{g}$ with coefficients in the first integral homology group of the boundary surface $\partial H_{g}$ for $g\geq 2$.