Homology action of a Dehn twist
= Homology action of a Dehn twist
{title2=$u\mapsto u+(\gamma\cdot u)\gamma$}
If $\gamma\cdot u$ uses the ordered-tangent orientation convention for <algebraic intersection number of curves on an oriented surface>, a <right-handed Dehn twist> takes $u$ to $u+([\gamma]\cdot u)[\gamma]$ on <first homology>. In particular a separating-curve twist acts trivially there.