  We show that recollements of module categories give rise to homomorphisms
between the associated Hochschild cohomology algebras which preserve the strict
Gerstenhaber structure, i.e., the cup product, the graded Lie bracket and the
squaring map. We review various long exact sequences in Hochschild cohomology
and apply our results in order to realise that the occurring maps preserve the
strict Gerstenhaber structure as well. As a byproduct, we generalise a known
long exact cohomology sequence of Koenig-Nagase to arbitrary surjective
homological epimorphisms. We use our observations to motivate and formulate a
variation of the finite generation conjecture by Snashall-Solberg.
