Retractions onto series-parallel posets

The poset retraction problem for a poset PP is whether a given poset QQ containing PP as a subposet admits a retraction onto PP, that is, whether there is a homomorphism from QQ onto PP which fixes every element of PP. We study this problem for finite series-parallel posets PP. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable, and, for such a poset PP, we describe posets admitting a retraction onto PP.