Retractions onto series-parallel posets

Abstract

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