Degree-one maps of Seifert manifolds into the Poincaré homology sphere

Abstract

This paper is devoted to the Legrand-Wang-Zieschang problem of minimal (in the sense of degree-one maps) Seifert manifolds. The main result is that the set of all possible map degrees from a Seifert manifold to a manifold with a finite fundamental group whose base is a sphere or a torus depends only on residues of parameters of exceptional fibers of the Seifert manifold. The minimality of some Seifert manifolds is proved by using this theorem.