Retractions onto series-parallel posets Original Research Article

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