Let $S_{g,b}$ an orientable surface with genus $g$ and $b$ boundary components and $S_g^b$ be an orientable surface with $b$ punctures.

Denote by $PMCG(S_g^b)$ and $PMCG(S_{g,b}) $ the pure mapping class groups, that is, the group of orientation preserving homeomorphisms of the surface fixing the punctures or the boundary pointwise modulo isotopy.

Is $$0 \to \mathbb Z^b \to PMCG(S_{g,b}) \to PMCG(S_g^b) \to 0 $$ a split short exact sequence ?