  It is well-known that the point cohomology of the convolution algebra
$\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result
by obtaining splitting maps whose norms are bounded independently of the choice
of point module. Our construction is a by-product of new estimates on
projectivity constants of maximal ideals in $\ell^1({\mathbb Z}_+)$. Analogous
results are obtained for some other $L^1$-algebras which arise from `rank one'
subsemigroups of ${\mathbb R}_+$.

Functional Analysis;Commutative Algebra