We determine the first homology group with coefficients in $H_1(N;\mathbb{Z})$ for the mapping class group of a non--orientable surface $N$ of genus three with two boundary components.
The first homology group with twisted coefficients for the mapping class group of a non-orientable surface with boundary
The twist subgroup of the mapping class group of a nonorientable surface
A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}
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